Tech Hiring Manager here. There've been quite a few speculative answers, so I wanted to provide a different point of view for you to consider.
First, I've seen this happen a few times successfully recently. I normally hire "hot" roles, now focused on cloud engineering. While we offer good rates, when you work in a hot field, our assumption is you've gotten multiple job offers, and we do our best to be competitive. That said, on a monthly basis what is competitive could radically change. As an example, Azure recently has seen a salary spike for senior architects. We found out because one of our candidates politely quit a day after joining because he got a higher than anticipated offer.
We have a salary range we target for each role. Assuming the candidate does well in the interviews if they ask for a salary beneath that range, we give them a higher offer because we know they will leave us immediately when they get a better offer. If a candidate's request falls within the range, we continue with the interviews. If a candidate's request falls above the range, it is up to me to decide if their skill and the market support an increase. Depending on the amount of the increase, it may impact my staffing plan and budget, so I need to ensure their knowledge and practical experience would allow us to forego another position to help pay for the increase.
After a candidate has accepted an offer, they may come back and ask for an increase. If their skill is in demand, I assume we're competing against another company for the talent. I revisit their interviews with the interviewers and see if there's something which could support the increase. Some times, yes. Many times, no.
While I do assess a higher risk of flight for folks who ask for a bump immediately before starting, if I feel they aren't ethically sound to work on my team, I won't. However, if they have a solid explanation for the bump, I'll bring them on board. HOWEVER, all of my hiring contracts include a 90 day walk-away period. If I get a bad feeling about an individual during their first 90 days, I'll give them an opportunity to accept the other offer.
So, what's my advice? Be very careful. If your experience is weak, or the market doesn't support your new request, it will be denied and your original offer will get pulled. If they do accept it, you had better be able to prove yourself quickly, or could find yourself without any offers.