No-Cost Extension to T&M Severable Services BPA Call Order

I have a T&M GSA BPA Call Order for severable services that will expire at the end of the month. It is expected that there will be funding left over at the end of the POP. The funds used were no year funds. The Government would like to extend the POP to use up the remaining funds. I understand contracts funded with no-year funds can go past 1 year, however I am unclear as to the ability to extend a POP simply to use up funds. Additionally, the parent BPA expired last year so no new Calls can be written off of it. Is it permissible to extend the POP of a T&M severable services contract to use up funds? I believe the justification would simply be that the services would stay the same (are in scope) and are still needed and not a case in which a deliverable has not been met. This is not a situation in which we would be using this as a bridge until a new contract is in place. In fact, there is an option year available, but the Government decided to not exercise it. Additionally, because the work would continue past the end of the POP, the vendor may increase their rates. Would this put us in a situation that is similar to a sole-source follow-on type of award?