Only thing I can think of is an EQ pedal. Maybe a modd'd boss one as i've heard they can be fairly noisy. Or Danelectro makes one that's fairly inexpensive.
These are characteristics (kinda) of strats, when compared to say, a Les Paul. You could try beefing it up, but truth be told, if you don't like the springy single coil twangy vibe, then maybe another guitar. Or a new pickup, and some amp adjustments. Heavier strings. Less mid scoop on amp. Block the trem. Avoid the maple neck..
Umm a Hot Rails in the bridge will make your Strat sound extremely huge and fat. Maybe some other humbucker. And i guess i can mention a hardtail strat sounds significantly more 'full' than a tremelo equipped one...my hardtail resonates a lot longer than the other one, and is a lot louder unplugged......food for thought i guess