I can answer this question from my experience
of applying for multiple postdoc positions
and accepting one of two offers.
A few years ago, I applied to around 6 postdoc positions.
The professor for one of the positions gave me an interview,
and gave me an exploding offer for position A with a one week deadline.
At the time, I felt that position A was the best fit for me,
so I was going to take the offer
and just withdraw from the other positions.
However, my PhD advisor advised me
to follow up with my other applications, just in case.
Upon his urging,
I sent a follow-up e-mail to each of the other positions
to which I applied, basically saying
I was wondering if there are any updates regarding my postdoc application? I would like to work with you, so I wanted to let you know that I just received an offer for another postdoc position, which I have to decide to accept by the date.
After I sent these e-mails, a few of the faculty told me that
they would not be able to make a decision quickly
and so would not be able to give an offer.
One of the faculty decided to give me an interview,
and eventually gave me an offer which I accepted.
I am thankful for my PhD advisor's advice
which led me to a position B which I felt was
a better fit for me than position A.
I am also thankful that the faculty at position A
gave me one week which was a reasonable time frame
for me to contact the other positions
and to work out an offer which I eventually accepted.
When you receive a firm offer,
you can politely let the other recruiters/faculty know
that you need to make a decision soon.
If they are interested in you,
that may spur them to act more quickly
to give you and interview and offer.