箱を開けてもいいですか。

box; case; chest; package; pack; car (of a train, etc.); shamisen case; shamisen; public building; community building; man who carries a geisha's shamisen; receptacle for human waste; feces (faeces); counter for boxes (or boxed objects)

indicates direct object of action; indicates subject of causative expression; indicates an area traversed; indicates time (period) over which action takes place; indicates point of departure or separation of action; indicates object of desire, like, hate, etc.

to open; to bare; to expose; to stretch

too; also; in addition; as well; (not) either (in a negative sentence); both A and B; A as well as B; neither A nor B (in a negative sentence); even; as much as; as many as; as far as; as long as; no less than; no fewer than; even if; even though; although; in spite of; further; more; again; another; the other

good; excellent; fine; nice; pleasant; agreeable; sufficient (can be used to turn down an offer); ready; prepared; profitable (e.g. deal, business offer, etc.); beneficial; OK

be; is

indicates a question (sometimes rhetorical); or; whether or not; some- (e.g. something, someone); indicates doubt, uncertainty, etc.; emphatic prefix; suffix forming adjectives or adverbs; in that way