So the Pseudo-Tiering System was made to be able to give a technical statistics to dream characters such as Madotsuki, since making a profile on just the non-dream aspects would be next to impossible and a lot of the interesting indexing comes from the dream world.
In the initial revision thread it was made clear you can't pit these characters in versus threads due to them being well, not real. Though this was back before versus threads were actually officially re-established and since they're fully established as just for fun I think it should be fine to use them in threads, there are some things to note though.
- The fight must always be in a way that makes sense, for example using Madotsuki again, the fight would take place within their dream world as that's the only place they "exist" truly.
- The fights are effectively the equivalent of how Ocarina of Time 3DS does battles, where we assume the character themself is dreaming and has access to all of their abilities within the dream. Otherwise there'd be no real way to say they get affected by any of the abilities used by the pseudo-tier character. The same applies for digital world characters by the by, it would just be assumed similar to how Danny Phantom entered the digital world to help inside of the game with all of their abilities kept.
- Can they be added to the Strongest Tier List? I'm not too sure of this, I could see making a separate list that allows pseudo-tiers on it though.
That's about all for this list.