It is possible. It is strongly not recommended.
It is possible, because these cables are simple copper wire. If you know how to splice wiring, and know how to put your own ends on the cables (many computer experts have been shown how to do this), you could make a Y-shaped cable that does this. As long as only one computer is turned on at a time, the switch would not likely notice the difference between that setup, or a setup involving multiple computers.
However, having three or more devices on a single connection is not within specification of how Ethernet is expected to operate. Computers (or other Ethernet-capable devices) are expected to receive electrical signals and to respond, and full-duplex Ethernet is made with the idea that there is only one response. Maybe half-duplex Ethernet would work, but you'd likely get a bunch of Ethernet "collisions", which are the main reason why people ditched hubs in favor of more complex devices, called (dumb) switches, long ago.
If your goal is to get two computers to share the connection at the same time, that goal will not work. A much better way would be to daisy-chain multiple switches. (Note: I'm not necessarily suggesting that, either. There can be limits related to this. A more professional/expensive solution may be to get a different switch with more ports.)