3 Offers in the first week, indicates you have something desirable. It won't take long.
I think the message has to be clear to the Agent....... You can instruct him to inform clients that the minimum his client will entertain is $xxx, get him to hand client a comparable sale list.
If at all possible.... don't let your agent know you have committed elsewhere, most (not all) will see that as an expressway to a quick sale.
And although I do not work in residential real estate, I have been a licensed agent for over 20 years.
PS: I'm not a fan of offers over, like others have said, all you will get is the minimum.... A fair and reasonable asking price is far more beneficial.