Pentium on a 386 motherboard

I was wondering what would be the ultimate upgrade for my 386 motherboard. It has a 386 CPU soldered-in, an unpopulated 386 PGA socket and a socket for either 387 FPU or 486 PGA or (might take a Weitek as well - not quite sure) and even might have a soldered-in 486SX PQFP. Plenty of options...

But how about hacking a Pentium in?

Nothing about this makes any sense, and yet, it's just plain awesome.