Pushing back internship

I likely (dont know 100% yet) have an offer for summer with a company in low-mcol that has a very high RO rate and good salary... so i really want to take it. but the company is not prestigious/unknown and not in my ideal location, regardless i need the RO for financial and job security reasons. Im still applying to other summer internships. Id like to do a f500 or faang or something ml related internship before i graduate to get myself more options and leverage when looking for NG roles. Would it be normal for a large company to allow you to push a summer offer into the fall? or should i just stop applying once i get the offer and wait for fall openings?