I don't know how you would alter the 2nd PS's wiring to connect it to the first, but I'm sure it can be done. Root around some of the o'clocking sites & I'll bet you'll see someone' diagram or whatever. Lot's of people with Peltier's use 2 PS's.
But here's a suggestion - and this is only workable if one of the PS's has an AC out connector on it (like for connecting your monitor to for its power source) like some PS's have. What I did was connect an extension plug to the AC out connector and hooked up some auxiliary components to that. The thing is that the line is always live, so you might want to put a switch in the line and you'd have to remember to turn it on and off. The idea is to run the 2nd PS off the 1st by connecting it to the 1st's AC out. If you are using a Peltier, where condensation is an issue, you might have to think very carefully about how such a setup is connected, since you are bound to forget that 2nd switch from time to time!