Can I keep my house on the market after accepting an offer?

You can do this, provided the offer to purchase includes the 72-hour clause, which it usually will.

The 72-hour clause means you can continue marketing your property. So what happens if you receive a better offer? You have to give the original buyer 72 hours notice. If they’re unable to fulfill their obligations (as stipulated by the offer to purchase) within that period of time, you will be able to accept the new offer.

The buyer may ask to remove the 72-hour clause but there’s no obligation on you to do this. You want to give the buyer an incentive to fulfill their obligations timeously.