[subject] + 未尝不 + [verb / adjective]
[subject] + 未尝没有 + [noun]
[subject] + 未尝 + [verb] + 过
未尝不 is a double negative that makes an understated "yes": "it is not that it isn't", so "may well be" or "not necessarily a bad thing". It goes before a verb or an adjective, and belongs to writing and careful speech.
The writer is usually turning a negative-looking situation round, so the sentence often follows a concession.
未尝不可 is a fixed phrase: "it's not out of the question", "that could work".
With a verb of wanting or knowing, 未尝不 admits something hidden, and 只是 often follows with the real obstacle.
Before a noun the form is 未尝没有: "not without".
Without 不, 未尝 + verb + 过 is a literary "never". You meet it in essays and older texts, not in speech.
未必 doubts a positive: "not necessarily so". 未尝不 grants one: "not necessarily not". They point in opposite directions.