It's like peanut butter and jelly... where you have to make the jelly before you put 'em together.
For those of us with a long memory this problem's been around for a while - since the DX days when there we no FX at all.
One of the nice things about many outboard multi-effects processors now is that they can be midi controlled and selected, so you can in practical terms, tailor your effects just by picking a program, or as part of the EXT program change sent when you select a combi.
It takes a lot of work. You have to integrate 2 systems and you might need to make some compromises to do it, but you'll be taking most of the limitations off your machine, which is worth the effort.
You can go cheap with something by Behringer and get all kinds of delays, flangers, 'verb, slapback, etc., and you might want to explore guitar effects (again look for something midi selectable) if you're into distorted or tube driven sounds.
DX used to be able to send a "mapped" program change. On Triton family, I think your best results would probably come from setting things up in combi mode - set up FX to something like channel 16, then you can send a program change to select the appropriate effect(s) for that combi. Note content shouldn't matter, but other controllers might (will!), so you'll want to read up on the 'MIDI Filter' section of the manual.