What you have to keep in mind is that the global period is a component of payer reimbursement policy - it isn't a coding guideline or rule. When a payer organization, such as CMS, sets a global period, it is making a decision to include the post-operative services during that period of time into their payment for the procedure. The decision to extend or not extend the global period is based on the payer's decision as to what they are including or excluding from that payment rate. It's been a couple of years since I reviewed payer global surgery policies, but if I remember correctly, there are some variations from payer to payer as to whether or not the 78 modifier resets the global period. Payers that don't start a new global period may reduce the surgical payment for the procedure that is billed with that modifier because they are excluding post-operative services from that payment.
So to answer the first question - no, the provider does not have the option to extend a global period - it's a payer decision and not the provider's. If the provider is participating with a particular payer, then they are contractually bound to that payer's policies and obligated to accept those rates as payment in full. Your modifiers must accurately reflect the services provided, and the payers rates either do or do not include post-operative services based on your billing. You'd need to refer to the specific payer's policy to know which is the case.