I've never tried growing (zucchini & yellow) squash before --at least not intentionally. They're all growing well, getting bigger which in turn causes them to be heavier, become unbalanced and flop over. I know some plants, such as tomatoes, like to dig their stems further into the soil to grow more roots, etc. while others need a nice dry exposed stem and would otherwise rot.

How do squash feel about it?
Is it safe to support the plants by mounding additional soil/mulch higher up around the base? I understand once the vines start running they can/should be buried and will sprout more roots so I assume this should be OK but thought it may not apply so close to the crown and so a good idea to check first.