Is it possible to add custom potion ingredients and have them use potion effects from other mods?

Check potion_map part of the config, that's where all potion ingredients are defined and you can add more in there. Based on what I can see it should be possible to add potion effects from other mods as well, but I haven't tested that so be prepared for potential crashes.
If you run into any let me know.

Can you provide some examples on how to add potion effects from other mods? I've used extraalchemy:dislocation but that doesn't seem to work.