Smashboards

One of the characters should be a bizarre chimera between Sam Winchester (Supernatural), the Eleventh Doctor (Doctor Who) and Sherlock Holmes (Sherlock)

Also, that Dashcon stage sounds absolutely awful, and I stubbed my toe by accident almost immediately after reading your post, so I'm holding the Mysterious Yellow Liquid responsible

I feel like shipping would have to be a mechanic somehow. Maybe in teams matches certain pairs of characters get special bonuses like if you pair Dean and Castiel they get 'no more internalized homophobia' which gives them better defense or something. Steve and Bucky could get 'I'm with you till the end of the line' that makes them stronger but if one dies the other goes with them. Etc etc. There would have to be at least 2 versions of the Onceler and like 5 versions of Sans.

the shipping idea goes hard actually, it makes me think of the "netsu" system from tekken tag tournament 1 where characters go into the "rage" state sooner depending on their relations with each other, like how paul and law go into rage when one of them only takes three hits when they're put on the same team

There are spirit-like collectables that boost your stats but there are only two types: seme for offense and uke for defense. Instead of characters these are objects like Yaoi Paddles or pentagon tattoos from Supernatural.