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If I need check bag, will firm reimburse for checked bag fees. I am going for a few interviews in a row and cant fit stuff into carry on

Yes, especially if you are doing multiple interviews. It's cheaper for Firm A and Firm B to split [airfare + $50] than it is for them to each fly you out. If a firm won't reimburse this on a SA interview trip, they are horrible tightwads who you don't want to work for.