I have a saying for times like these, "Too busy to make money"
I know how hard it is to turn a customer away or even put them off and schedule them out a few days. I don't want to lose a customer either...BUT, when you try to cram too much work into your shop, ARO drops, things get rushed, missed, messed up. Inspections get skipped and the bottom line plumets.
For every new customer that you "worked" in, you lost another by short changing their experience with your shop.
It's not an easy balance to find and lord knows I have not mastered it, but balance is what we should be seeking.