Dragonmaid really is not the best engine to be running if you want to get a Level 9 monster on board easily. I guess that this realistically is more of a Summoner of Illusions showcase for Prediction Princess than it is a "Dragonmaid Prediction Princess" Deck, but I'm still combing through all the Level 9 monsters in the game and putting them into a Prediction Princess Deck. Are there any actual benefits to playing Dragonmaid in Prediction Princess? Literally no. The Main Deck Dragonmaids in Chamber Dragonmaid and Parlor Dragonmaid are very Normal Summon reliant and there is also no real good way to search a Dragonmaid monster through in-archetype cards except for Kitchen Dragonmaid which is yet another Normal Summon who is one of the worst searchers I've seen for an archetypal card. This Deck is using them in order to search Dragonmaid Changeover which Fusion Summons House Dragonmaid out of the Extra Deck, getting you a Level 9 monster on the field whose Type and Attribute are perfect for World Legacy Monstrosity in this Deck. Yes, the days are over for us where we "need" to use Monstrosity because of Master of Ham access off of Instant Fusion, but we are playing the best of both worlds in both a Monstrosity line and Instant Fusion for Master of Ham in this Deck. I do really like Ham Prediction Princess and going all in to search for Instant Fusion for Ham access and I do think that is much better than bidding on Monstrosity, but I am currently experimenting with Prediction Princess making use of the various Level 9's in the game and seeing if they can actually make a functioning Deck.
For our Main Deck monsters: 3 Ash Blossom & Joyous Spring. 3 Prediction Princess Tarotreith and 1 Prediction Princess Tarotrei. Again, I think that playing a combination of 5 Prediction Princess Ritual monsters consisting of some number of Tarotrei and some number of Tarotreith is a good Ritual Monster concentration for the Deck. However, I've had some time to dwell on Tarotreith and I figured that since it is the more "important" of the two Rituals for plays on your opponent's turn, I'd rather be playing a higher concentration of it. Tarotreith can be Ritual Summoned or Summoned from hand or GY via Tarotrei's End Phase effect. On Flip, it can Summon a Flip Monster from Deck face-down and as a Quick Effect, it can Flip any number of your monsters face-up or face-down. Tarotrei can Quick Effect Flip a monster face-up or face-down and can Summon a Flip Monster from hand or GY in face-down Defense Position during the End Phase. 3 Prediction Princess Bibliomuse which on flip adds a Prediction Princess monster other than itself and a Ritual Spell from Deck to hand. If it's Tributed and sent to GY, it can Summon itself back face-down, and while on field, it gives your Ritual Monsters targeting and destruction protection. 2 Deus X-Krawler which negates all of your opponent's monsters' activated effects on field after it has been flipped face-up, and when it's destroyed on field, it can add a Level 9 with a different Type and Attribute than it from Deck to hand. I would play 1, but having another copy in Deck is good in case you drew one in your opening hand to still have Monstrosity live. You could play 1 Pot of the Forbidden in place of the second Deus X, but that's up to you. 3 Manju of the Ten Thousand Hands which adds a Ritual Monster or Ritual Spell from Deck to hand on Normal or Flip Summon. When you don't have access to the Dragonmaid portion of your Deck or access to World Legacy Monstrosity, Manju helps you get to more of your Ritual pieces for your Prediction Princess plays. 1 Dragonmaid Ernus which is pretty much only here as a way to Special Summon a Level 4 or lower Dragonmaid from hand by discarding it. Also, I guess it also acts as a Dragon monster for Fusion Material for House Dragonmaid. You could cut this card if you want, but having a way to get a Dragonmaid onto the field without using your Normal Summon and having an extra Dragon for Fusion Material just in case is pretty alright. 3 Chamber Dragonmaid and 3 Parlor Dragonmaid. Chamber adds a Dragonmaid Spell/Trap from Deck on Summon and Parlor sends a Dragonmaid card from Deck to GY on Summon. Chamber will usually be searching Dragonmaid Changeover for a Fusion Summon whereas Parlor will be sending either Changeover or Dragonmaid Tidying. If you draw Parlor and another Dragon, you can send Changeover, Changeover bounces Parlor to hand to add back itself, and you can Fuse into House Dragonmaid from there. If you draw say Parlor and Foolish Burial, you can Normal Parlor to send Tidying, use Foolish to send Chamber, Tidying banish from GY to Summon Chamber from GY, and Chamber search Changeover for a Fusion Summon. 1 Summoner of Illusions which on flip Tributes another monster to Special Summon a Fusion Monster from your Extra Deck which is destroyed during the End Phase. Mind you that this is a MANDATORY effect, but it works wonders in a Deck like this. So what are your options? Well, your best options are monsters who don't have an important effect that activates specifically on Fusion Summon, a way to negate cards and/or effects, or a generally good effect, but most importantly, they cannot say "Must be Fusion Summoned" or "Must first be Fusion Summoned". Let's go through them:
~ Naturia Exterio - This card is basically infinite Spell/Trap negates by banishing a card from GY and sending the top card of your Deck to the GY.
~ Invoked Mechaba - This card can negate a Spell/Trap Card or monster effect by discarding a card of the same type. It's a very solid piece of interruption and negation.
~ Dragonmaid Sheou - An omni-negate that bounces itself back to the Extra Deck afterwards to Summon a House Dragonmaid from Extra Deck. Excellent for this specific Deck.
~ Eldlich the Mad Golden Lord - He cannot be destroyed by any card effect, including its own destruction via Summoner of Illusions's effect during the End Phase. And if he sticks around, you can Tribute a Zombie, most likely being himself, on your turn to take control of a face-up monster your opponent controls, period.
~ Despian Proskenion - During the Main Phase, it can Quick Effect banish a Fusion, Synchro, Xyz, or Link from your opponent's GY or Special Summon it to your field.
~ Gaia Prominence, the Fierce Force - It's a bit of a stretch, but by discarding a card, you can negate an opponent's activated monster effect in the hand or GY.
~ Grapha, Dragon Overlord of Dark World - This substitutes an activated monster effect or an activated Normal Spell/Trap Card of your opponent with "Your opponent discards 1 card." This is a bit more situational as you can't activate this effect if you, yourself, have no cards in hand because that would make it an illegal activation.
~ Mamonaka the Vaylantz United - During the Main Phase, it can Quick Effect target an Effect Monster in your opponent's Main Monster Zone and place it face-up in the Spell/Trap Zone in the same column as a Continuous Spell, but if that Zone is occupied, it's instead destroyed and your opponent is burned equal to its ATK.
~ Tearlaments Kaleido-Heart - This card targets and shuffles a card your opponent controls into the Deck on Special Summon. It isn't as good as some of the other monsters here, but it is definitely a consideration somewhat, and it also is a Level 9 so it can technically act as a Monstrosity target on your opponent's turn.
~ Red-Eyes Dark Dragoon - It cannot be destroyed or targeted by card effects, period. Yes, this includes Summoner of Illusions's End Phase effect. You cannot pop cards with its first effect because it was not Fusion Summoned, meaning no Normal Monsters used for it Fusion Summon, but it is still an untargetable, indestructible omni-negate once per turn.
~ Mirrorjade the Iceblade Dragon - If you are willing to play another Albaz Fusion in the Extra Deck, this card is a Quick Effect banish 1 monster on the field. And no, it cannot use its other effect to destroy all monsters your opponent controls during the End Phase if your opponent gets rid of it because it wasn't Fusion Summoned.
~ Rindbrumm the Striking Dragon - This card negates your opponent's activated Fusion, Synchro, Xyz, or Link Monster's effect and returns a monster on field to the hand.
~ Tearlaments Rulkallos - Rulkallos negates the activation of a card or effect that would Special Summon a monster(s) and sends a Tear from hand or field to GY, including itself.
~ Dark Cavalry - As a non-once per turn, it can discard a card to negate an activated card or effect that targets a card on field. This includes your opponent targeting their own cards as well which gives it a lot more utility, but just like Gaia Prominence, it is only a consideration.
~ Millennium-Eyes Restrict - When your opponent activates a monster effect, it can target an Effect Monster on your opponent's field or in their GY and equip itself with that monster, gaining ATK/DEF equal to that monster's ATK/DEF and it negates the activated effects of all monsters with the same original name, and prevents them from attacking. Because we are also playing Instant Fusion in this Deck, it wouldn't hurt much to play this card because you can either use it as interruption or protect yourself against handtraps on your turn.
For Spell/Traps: 1 Instant Fusion. 3 Pot of Prosperity. 3 Underworld Ritual of Prediction which can Ritual Summon a Prediction Princess from hand or GY face-up or face-down and it can banish itself during the Standby Phase to Special Summon a non-Ritual Prediction Princess from Deck face-down. 1 Foolish Burial to send a Dragonmaid for reasons I stated earlier or it can send Tarotrei or Tarotreith because Underworld Ritual can Ritual Summon from GY. 3 World Legacy Monstrosity which can Special a Level 9 from hand or target a Level 9 on field and Special Summon 2 Level 9's from Deck with a different name, different Type, and different Attribute. 1 Dragonmaid Changeover which can Fusion Summon a Dragon Fusion Monster using monsters from hand or field. If it's in GY, you can bounce a Dragonmaid you control to your hand and add this to your hand. 2 Dragonmaid Tidying which can target a Dragon monster you control and a card your opponent controls or in their Gy and return them to the hand. You can use this card for interruption if you draw it, but as for its GY effect, you can banish it to Special Summon a Dragonmaid from hand or GY which may come up in your combo. And finally, 3 Infinite Impermanence.
Extra Deck: 1 Naturia Exterio. 1 Dragonmaid Sheou. 2 House Dragonmaid which is our Level 9 target of choice for Monstrosity in this Deck. It can be made with a Dragonmaid and a Dragon monster. 1 Red-Eyes Dark Dragoon. 1 Master of Ham which can be Summoned via Instant Fusion and on Fusion Summon, it can Special Summon a Flip Monster from Deck face-down which gives you access to Prediction Princess Bibliomuse. 1 Alligator's Sword Dragon which can also be Summoned via Instant Fusion. If you draw Monstrosity and the Dragonmaid line, you don't need to go into Master of Ham for Bibliomuse, in that case, you can Summon Alligator's Sword Dragon for a Dragon for Fusion Material for House Dragonmaid. Your other options are Curse of Dragon, the Magical Knight Dragon and Darkfire Dragon. 1 Herald of the Arc Light to send off of Mereologic Aggregator for a Ritual Search. 1 Divine Arsenal AA-ZEUS - Sky Thunder. 1 Infinitrack Earth Slicer which can detach any number of cards to pop the same number of cards and it can attach a monster it destroys by battle to itself as Xyz Material which makes it good for board clearing and making Zeus. 2 Mereologic Aggregator which sends a monster from Extra Deck to GY on Xyz Summon and it can detach materials to reattach monsters from GY which means you can recycle Herald for more searches. 1 Laevateinn, Generaider Boss of Shadows and 1 Jormungandr, Generaider Boss of Eternity for a Rank 9 option. 1 Gravity Controller to Link off Aggregator.
Side Deck: 2 Nibiru, the Primal Being, 3 Thunder King, the Lightningstrike Kaiju, 1 Kurikara Divincarnate, 3 Triple Tactics Thrust, 2 Dark Ruler No More, 1 Harpie's Feather Duster, and 3 Evenly Matched.