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Has there been any success in transmitting two simultaneous FM signals? I am assuming if the phase is correct, and the signals are identical, it would be possible.
That would be really nice if newer repeaters could find a way to broadcast two signals on the same frequency from two different locations, giving extended coverage without sacrificing more coordinated frequencies. RX is already solved with voting receivers, but I haven't heard much on the TX end.
Yes, it's very possible, and in fact, it's quite commonly done in commercial FM broadcasting, in order to provide full coverage for major metropolitan areas.
The key to making it work is to make sure that the modulation (not the carrier) of two transmitters is time-aligned in the "overlap" region where the signal levels are approximately equal (e.g., within 6 dB). Outside this region, an FM receiver will "capture" one transmitter or the other, but inside this region, it will randomly jump from one to the other. But as long as the modulation is time-aligned, the output of the detector is essentially the same regardless.
That isn't to say that there aren't many compromises in such a system. Given the variabilities of terrain, etc., it's impossible to get optimal time alignment in all of the overlap regions. Considerable effort goes into modeling the placement of the transmitters (and to some extent, adjusting their power levels) in order to position the less-well-optimized regions away from high-traffic areas.
In the distant past (1990s), I worked for a company that sold networking equipment to commercial radio stations, and I designed the part that implemented the required timing control.
If you transmit the same FM signal from 2 locations, the receiver will experience a similar effect as FM multipath (when a single FM transmission arrives at the receiver from different paths, mainly due to reflection of the signal). The result is normally a very distorted audio signal.
Single frequency networks (SFN) is the term used for multiple repeaters on the same frequency. SFN is possible and is actually used with OFDM transmissions such as digital TV. But, as stated above, it is not possible for FM transmissions.
We should distinguish between ways of having multiple FM transmissions on a single frequency.
CAPTURE EFFECT Transmitter frequencies in FM broadcasting networks are allocated relying on the limiters in FM receivers to separate a stronger signal from weaker signal(s). This is a key advantage of FM over AM (that exhibits no capture effect i.e. any interefering signals are heard proportional to their relative strengths) and is well described in Dave Tweed's answer. The chopping effect sometimes heard on a mobile receiver in an area where the desired signal is not strong enough to reliably saturate the limiter has been called the "picket fencing" effect.
QUADRATURE SIGNALS The I (in-phase) and Q (quadrature- or 90 degree phase) components of a transmitted carrier can be modulated and demodulated without interference, potentially allowing two independant FM transmissions. This works only with a single transmitter antenna because there must be no difference in receive path delays that would change the quadrature phase relationship, and the receiver needs a special synchronous demodulator. This is common practice with QPSK data transmission but unusual for sudio.
SUBCARRIER(S) Since FM transmitters are usually allowed generous bandwidth (band limiting increases distortion) there is the possibility of adding an ultrasonic sub-carrier to the audio modulation. Broadcast stations add subcarriers for many purposes that include a channel-difference signal for stereo receivers, data broadcasts, transmitter/studio telemetry, reading service for the blind and (now defunct) Muzak distribution.
The above are continuous multiple FM transmissions on a single frequency. I do not count signal sharing formats such as TDMA (Time- ) FDMA (Frequency- ) or CDMA (Code-Division Multiple Access) that are used in cellular telephony nor OFDM whch is a wide band multi-carrier modulation.
