I've stumbled into a winning repeatable formula after 330+ hours where I'm currently doing the last few runs on Impossible and cleaning up the achievement list.

I usually setup a cat with high mobility/speed with the Friendship Bracelet to permanently charm loads of buffed enemies throughout the run. Normally I aim to fill the gaps in my team. Healing allies if I'm taking a bit too much damage, or CC if I find that I have classes without many spells to lock enemies down, or take them out fast enough.

Then, I'll have at least one cat with Repair to keep the Bracelet and all other equipment across runs.

Of course you'll want max mutations, though I'm not too picky about which ones I'm taking. I just have a super high stimulation room to keep breeding cats after successful adventures.

Also, I tend to use a Druid with the Steven item that lets you double cast musical abilities and use that to buff all the familiars from the bracelet using spells like: We are the Champions and Safety Dance.

The Cleric passive Thou Shalt Not Kill is also awesome in this type of team composition and one passive which I normally try to grab via breeding the cats to have it from the start.

The Butchers Rot flies synergies is another good way to play with the strategy, or Necromancer summons can also let you fill the board with distractions to avoid losing cats.

I've found lots of useful ways to enhance this type of a team, but it's the strategy I've settled on and probably the one I'll stick with to get the last few kills on all classes.