Not easily. You'd need a buffered AB box, one to go after the guitar, switching between
the JMP1 input and the TSL input. AND you'd need a way to bypass the fx loop. As for the
processor you'd have to put it between the guitar and the AB and use it in series.
Honestly, if I were you I'd either...
1. Sell the JMP and the TSL and buy
something that has channel switching that you can live with.
2. Buy a power amp and
speaker for the JMP1.
In option 2 you can either run the FX in series but what
you might consider is running them through the FX loop of the TSL, and then using an ABY
box to add the JMP for gainy sounds, but leaving the clean running underneath with the fx
on the clean sound. It might not be what you want, but it can be a very cool sound.