First of all, I just want to make something clear, just in case. If you are getting another frog, it should be because you want another frog, not because you think your current frog needs a friend, because he simply don't. If anything, it's someone to compete for food with. He will not benefit from another frog, but then again, he will not suffer from it either in any way, as long as it's another White's, which brings me to the next point. If you want another frog, it should be another White's tree frog, not another species. There are a few variations of White's. Here's the one I know of:
"Ordinary" White's
Albino White's
Blue phased White's (just a little more blue in it's skin)
Blue eyed White's (I thought this was just someone misspelling blue phased, but apparently it's a variation where the eye-colour is a bit different)

Also remember to quarantine the new frog (at least 30 days, more if you can) before adding him to the ordinary enclosure. This is to prevent any disease to transfer from the new frog to your old, which might kill them both. If the quarantined frog shows any kind of illness during the period, it'll not only spare you old frog, it'll also be easier to treat him correctly.

I hope you find what you are looking for, and hopefully someone else can add a little more useful information for you!