If I'm in a situation where a standard raise (2x BB + 1 BB per limper) is going to put me in a situation where I'm going to have very low SPR on the flop or leave me short stacked if I fold, I lean more towards either folding or jamming. With 15-20 BBs, you can still fold hands like 27, even with a tight image. I might shove 27 with 15-20 BBs if 6-7 players limped in since the pot (with antes) represents a large percentage of my remaining stack and I think I can pick up the dead money easily. Otherwise, I'll stick with a wide range, but with hands that have some potential to do well. Hands like J5s can hit a flush, 610s has some flush and straight combos, etc. If I'm short at ~10 BBs, then yeah, I'll shove ATC if 4 players limped in before me as the pot w/ antes = ~50% of my stack.
The only hands I wouldn't shove in your situation with 15-20 are KK+. Instead, I go for the standard PFR and try to get some value for the hand. SPR will also be low, so if I have 15 BBs, with a standard raise, I'll have ~9 BBs behind with a pot of ~16 BBs, so its possible to get the rest of the money in at some point. And if I get someone to jam over the top preflop, that's even better.