The phrase "unlimited number" means an indefinite or large quantity, with no specific limit. It refers to a countless amount or something that is not restricted or limited by any boundaries.
The potential cost of allowing unlimited numbers of charter schools, which operate on public dollars but are run as non-profits, isn't known. (ncpolicywatch.com)
No just one bank account for unlimited number of properties. (biggerpockets.com)
You are entitled to request unlimited number of revisions and claim full refund if a completed paper was not delivered at specified deadline. (customcollegeessays.com)