You can try. If your current contract is about to expire, you can state the terms under which you're willing to extend it. Just realize that if the buyer is attempting to finance it, changing the terms may start the whole loan approval process again, likely postponing closing even longer.
If the buyer doesn't agree, or they feel they are being treated poorly, they may just let the contract expire and allow you to start over with another buyer, which isn't always as easy to find as it seems. Once a home has been off the market and it comes back on, people ask, "what happened" and get suspicious that there may be a problem with the house.
But if you're representing the buyer, why would you want to (presumably) raise the purchase price? It seems that would be of interest only if you were representing the seller. Bottom line -- this question needs more info supplied before it can be properly answered.