What happens right after an offer is accepted?

Usually, if it's an offer that both parties are happy with, and want to go ahead with, a contract is drawn up (by attorney) sent to buyer to sign, and then they put money in escrow, then the contract is sent back to seller, who signs, and after that, the property is supposed to be not shown any more, and is considered "in contract".

There's no reason you cannot continue to show 'for backup' after an offer has been accepted. Until the contract is signed by both parties there is no binding deal. The broker should tell any other prospective buyers that an offer has already been accepted. It sounds like your broker is doing a good job--ask him/her what he suggests.

Thanks to both of you for the input. Based on your responses, my guess is my broker will continue to accept viewing appointments, but no longer invest the energy into having open houses. I will have to see what he says. Thanks!

>Thanks to both of you for the input. Based on your responses, my guess is my broker will continue to accept viewing appointments, but no longer invest the energy into having open houses. I will have to see what he says. Thanks!

That would be the precise thing to do.
Open houses can very much annoy your prospective in contract buyer, it's hard enough to get from start to finish without fanning an extra flame.