My own personal experience is that I’ve grabbed six new cards in the last year and a half and the impact has been moderate; my score has dropped, but remains good. The impact immediately afterwards (as in the following days/weeks) is larger, but then it shortly recovers much of what was lost.
I’ve also recently taken out a mortgage and the card history was no problem for any lender that I dealt with, although I was required to drop the total available credit limit down to $20k. The loan having been approved I was able to pick up another card last week no problem either.
I would second the suggestions to keep an eye on your credit score (credit savvy will even email you monthly updates for free; looks like they’re Experian) and ease off on the card acquisition if you notice a large drop even after a couple of months.