Probably the more realistic answer is as follows.
King build their GPS RX to support a specific - db gain, preamplifer that is housed insite the antenna. Garmin uses a different gain specification with theirs. So a King antenna won't work (well) on a Garmin and vice-a-versa.
Also the bigger issue is the voltage that is required to power the pre-amp in the antenna comes from whatever is connected to it. There are 2 different voltages that are in use today 3v and 5v. An antenna that wants 3v could be damaged by one that drives with 5, and a 5V antenna, when driven with 3V usually doesn't work.
All of this could be done with a "black box" in the middle of the devices and the antenna as long as you are "like to like - garmin to garmin, king to king". However, I know of no-one who is making a *cheap* duplexor for GPS antennas...
Nice Idea, but probably not plausable given todays environment.