。
Could you come in for an interview next week?
Literal
Next-week interview [for-に] come-honorific-[humble-receive-いただけ]-[question-ますか].
A business keigo request. おいで is the honorific form of 来る/行く/いる (literally 'honorable presence/coming'). ~ていただく is the humble equivalent of ~てもらう ('to receive [someone's action]'). Combined: 'could I receive your [honored] coming' — i.e., 'could you please come.' Layered politeness typical of formal business invitations.