I know that PM itself will not invalidate the Staples easy rebate generally. Then how about the combination of PM and coupon like $40 off 300, $40 HP trade coupon?

As long as there is no wording on the rebate like you will only get "price paid" you should be OK.

I haven't encountered any problems with coupons. Used lots of ink coupons on rebate items.

If you PM online/phone, then no problem, as the difference is a direct credit to your CC. In store, will typically result in a return/rebuy. Few know how to properly do the adjustment, so if you do this outside of the rebate term, then it will be invalid.