...There are solutions for transmit as well, but they are more complicated.
And MUCH more expensive.
It's a device called a control station combiner. They're intended for dispatch centers, etc. where there are a number of control stations used for repeater access, and a requirement exists to minimize the number of antennas used. They allow frequency agile radios (like trunking) to transmit and receive on a single antenna.
As I mentioned, they are expensive. They are also lossy, so there is a substantial performance hit that probably makes them a bad idea for amateur use.
A more affordable approach would be to use several RF rated relays, a sequencer, and a passive multicoupler. A multicoupler would feed the the receivers until either one is keyed to transmit, then the RF relays close the path from the transmitter direct to the antenna. The sequencer prevents the transmitter from actually being keyed until all the relays have been switched. Sounds a bit complicated, but it really isn't.