Do you mean one inquiry per issuer? Each issuer will pull from one or more credit bureau. If the bureau sees multiple pulls on the same day from the same issuer they may consolidate them into a single event, but if they see one each from four issuers there is nothing to consolidate.
Chase looks at accounts opened in the past 24 months (in addition to inquiries). If you have opened five in that period why do you think you are "close" rather than over their apparent limit?
So if I applied for 2 amex cards, that could be combined? But if I do chase, amex, citi etc that would certainly be 3 hp?