My Epi LP, I found out, is made of basswood with a maple cap (and a thin "flame" veneer over it). I've had it for years, and gigged it with it's own pups - sounded very good.
I don't knock basswood myself, my JV Squier strat seems to do a fine job made of it, but when my Mules didn't seem to do what I expected in the Epi, I did end up wanting a mahogany beast.
I tried a few Epis, but none of them seemed to greatly outshine the one I own, and then I found and bought myself a Japanese Tokai Love Rock - that definitely does what I was expecting :D It is heavy-ish, yeah, but I'm not too good a judge on that - I like a solid plank hanging off the strap :lol: (I'm a strat player after all!)
I do have to say though, my basswood Epi LP has a FAR better accoustic tone than my old Epi SG that is apparently made out of mahogany - that one's always been prone to sounding "boxy" when amplified unless you put a lot of effort into the amp settings... I don't gig anymore, and so haven't run it through a real amp recently, but I suspect that it'll still have that "issue" even now its got Riff Raffs.