I think if you actively want to play for a certain organization and you have received an offer from that organization that is where you hope other offers would land, there's little downside to getting it done.
The last time I changed jobs was the first time I actually had two places pursuing me at the same time. There was one job that I really wanted and another that was intriguing but I wasn't as into. My current employer made the first offer and it was a good one, so I took it and never looked back. The second place did make an offer several days later that was worth close to $10K more, but I was really happy with the first offer and had/have absolutely zero regrets.
I remember really fretting about it at the time, fearing I'd misplay my hand, make the wrong choice, etc. In the end, committing to the place I really wanted to be was totally the right thing to do.