OP likely has the space for a six speed Shimano Mega-range but with caution to chainwrap.

They are quite the deal and an excellent upgrade. I found a 7 speed version N.O.S. in the box for only $3. That of course is not the norm but often see them less than $20. For the 7 speed, I did have to get a longer axle and spacer.... found that too NOS in the freebie junk bucket at a LBS.