I have been interviewing for the past two months with a company X that is one of "The big 4", for a dream job. Successfully finished several interviewing rounds and now my last and most difficult round is scheduled for 3 weeks from now.
I was reached out by Company Y which is mature (+600 employees) recently and done 2 rounds that went really fast, and quickly I receive an offer from them. Things went fast and truly I was not asked if I am interviewing outside, all what I was asked was when is your availability time to start and I said a month after submitting a notice.
I would want Company X, and today I asked them if we can move the last round to an earlier time (end of next week), they said they will be more than happy to do so and will get back to me before the end of today.
I know that I have a lot to prepare for my last round with Company X, but I don't want to decline the offer from Company Y (or maybe I would?). And I know that accepting (signing) with Company Y then changing my mind is unprofessional and would burn bridges, I guess.
How can I "push" Company Y to two or three or a month from now? Basically, enough time to prepare for round 3 with Company X, do it and then hear back from them for whether I will be hired or not. Is it ok to mention the entire plan to Company Y? I don't want to sound like "Oups sorry I forgot to say that I am interviewing with a different company".