I agree with both answers given. You can, but will likely face legal ramifications as there will be a claim to the property with the accepted offer from the first buyer, therefore making it difficult for you to actually convey free and clear title to the second buyer (should the 1st buyer file a claim for performance against you). You could also accept the 2nd offer as a full backup offer (signed and accepted) with the contingency that the first offer must be legally terminated for the 2nd offer to go into effect. Consult a Real Estate Attorney
A 3rd option that most people do not consider, is asking the 1st offer to "walk away" and offer them some compensation for their trouble. If the 2nd offer is that much better, then this is a possible strategy to make it happen. You might even get the 1st offer to come up in price to stay in the game!
Keep in mind however, there is a lot of parts to an offer (price, terms, time, condition, ability to actually close etc...). $10,000 more from the 2nd buyer may not be worth it if the chances or success are slimmer, or you'll be rquired to do things you don't want to do (make repairs, etc)...