If you have any warm leads that are decision makers at a tech company, email them with the fact that you got an offer and what your timeline is. Or if you're part way through applying at places, now's a great time to email your contact an update.

If you haven't been keeping many irons in the fire, that makes the whole process of getting what you want way more difficult.

no company is going to say.. wow facebook made you and offer work for us instead right now.

I've interviewed hundreds of people and the biggest question is usually "Do you want to work with this person?" The interview process is more about how well the team thinks you'd work with them and not so much on your tech skills.

This is a totally reasonable comment. I definitely wouldn't expect one company to make me an offer just because another did, but I feel like, maybe incorrectly, having an offer in hand could potentially be persuasive to the other company to at least give me a shot.

I guess I'm more asking: Is there a standard way to get in touch with another company to try to at least use the first offer to get my foot in the door and (hopefully) avoid the super rigorous tech interviews in lieu of fit interviews?

You: I've been offered a spot @ FB/Apple/Google etc.

Our Recruiter: Neat, half of engineers have worked @ one of those places. So our tech screen process is...

I think the answer you are looking for is "No."

no that's just a stupid idea anyway. If someone came to me with an offer I'd wonder how crazy and/or stupid this person is and just say good luck at company X.