TPWK from the BB on somewhat coordinated flop?

Preflop
4 limpers, SB completes you check in BB with Th8d.

Flop : 10c-9s-3c. (6-way)

Do you ever bet this flop multiway?
When can it be OK to check-call a flop bet?
When might a check-reraise be motivated?

Also, how does the number of limpers influence your chosen line?

My thinking is that leading out here is very likely to get called, leaving me with a crappy hand OOP and no information.
Check-folding the flop is my standard play – though I’ll call if a muppet bets something stupid-small, like 1/3 pot. And I may call (or even reraise) if it’s bet by the button.

If I see a turn, I’ll give up to any flush draw that may hit. Only turn card I like is when I hit 2-pair.

Clearly, it is a very common situation and a proven spot for spewing chips…

Cheers,
Zal3