Not only is it possible, but it has already happened! Back in the 1980s, it became clear that the initial design of the world network did not foresee its expansion rate. At first, this apprehension led to the implementation of several remedial technologies. Eventually, the need for the new Internet protocol rose.
On November 25, 2019, the last free IPv4 (the exhausted protocol) addresses in Europe, post-Soviet states, and the Middle East were distributed. Henceforward, getting an IPv4 address is only possible if someone (for example, a closed company) frees one previously used. The new protocol, IPv6, can solve the problem. However, the issue of older devices being incompatible with the new protocol is the reason for IPv4 and IPv6 existing alongside for yet indefinite time.