It's certainly possible but it all depends on one's credit, the loan underwriting criteria, etc. As always, it's not just a single factor at play. There's isn't an X for number of cards that is "too many" in all cases.
cashback wrote:You can never have too many credit cards, unless they are all maxed out.
Too many is a subjective matter. For some, 1 card is too many. For others it's a larger number. It's not just a matter of whether they're maxed out or not but what the individual can reasonably manage.