The phrase "could possibly provide" is grammatically correct and can be used in written English.
It is typically used to express the idea of a potential or hypothetical ability to provide something. Example: "Although I am not sure, I believe that this company could possibly provide us with a solution to our problem."
The research in this paper could possibly provide useful information for the researches and engineers to design damping structures.
It conveys a fuller sense of Friedrich's enigmatic, landscape-centered art than any single museum or exhibition could possibly provide.
The EU's Water Framework Directive (WFD) could possibly provide the necessary motivational framework for instigating and enforcing Arundo removal in Portugal.
This particular cell had a combination sink and toilet, a water faucet and a towel bar/handle that could possibly provide an anchor for a similar suicide attempt.
Family members said they learned that a security camera was operating in a nearby laundry and could possibly provide information about the vehicles that hit Ms. Guzman.
So, then -- for the young man who is without parents or friends or home or romance or uncompromised elbows -- who or what life force could possibly provide succor?
A telemetric database could possibly provide a long-term profile of where a car has been and how it has been driven.
"Tom's personal preferences on his footballs are something that he can talk about in much better detail and information than I could possibly provide," Belichick said.
A Nickelodeon executive responded in an interview that the series was not intended for an audience of that age and that the study used "questionable methodology and could not possibly provide the basis for any valid findings that parents could trust".
The driver couldn't possibly provide change and there were no shops nearby.
It was soon realized, however, that the government could not possibly provide enough schools for all who required education, and it reversed its policy to some degree.
