I have used oscilloscopes for over 56 years. I have never seen anything like that. What is the purpose/use of such a thing? Your "3-channel isolating amplifier switch" seems to have three Voltage steps and each of your input signals is SWITCHED on during and superimposed upon one of these three levels. It appears to be a type of combined time and Voltage level multiplexing. But WHY? WHY would you want to do that?












?? Or, if that is not what it is doing, then WHAT?
As for triggering, you do not give enough information to allow an answer. I see several possibilities:
1. You have access to all three of the initial signals, which appear to be phase locked together as well as the combined signal from your "3-channel isolating amplifier switch" which also appears to be phase locked to the input(s). In that case, I would simply choose one of the input signals, the triangle waveform seems like a good choice, and use that for your trigger signal. But this ASSUMES that the input signals are what you show and not something else (like stereo audio and composit video, perhaps or maybe R, G, B video or whatever).
2. Your input signals are not always what you show (sine, triangle, and

) but can be any arbitrary waveforms including random noise. In that case, you need to look to your "3-channel isolating amplifier switch" for the possibility of a trigger signal. Perhaps as a separate output. Or you may need to modify it's circuitry to bring out such a trigger signal. (Side question: How is the frequency of the three steps generated? From one of the input waves? Which one? From some combination of all three? How are they combined? More questions along this line.)
3. Your input signals are not available and you do not have a trigger from the "3-channel isolating amplifier switch" and you can not modify it's circuitry to obtain one so you must trigger from that mess of a combined waveform. In that case and if your input signals do not change over time, then PERHAPS a low frequency filter or band pass filter can produce a trigger signal. I have been in similar situations and getting a good trigger was NOT EASY.
4. Oh heck, there are just too many more possibilities to keep going through all of them. Perhaps you can be more SPECIFIC.
But I have heard that things will be different, things will be BETTER when we have digital oscilloscopes.
.................
Oh, wait, wait ... we DO have digital oscilloscopes. So, what's the next iteration? Analog, digital, then _____! And when do we get IT?
I can't wait.