It depends on the type of transmissions. If the two antenna are for similar or overlapping bands then the noise from the second antenna will add to the the total signal and reduce the quality. The signal will also leak out the other antenna because there is essentially no difference between the tuning for a trnasmitting or receiving antenna.
(In fact in the days when television receivers had to be licenced, the authorities detected the heterodyning oscillator coming out of the antenna.)
If the signals are in different VHF bands you you can widen the coverage. If the antenna are for specific stations or different narrow bands they can usually be connected by a simple splitter.
If the two antennas are for widely differing bands like VHF and UHF you should connect them using a signal booster with separate inputs designed for the different bands.
Normally you won't be able to get signal from two transmitters having the same channel. However if you can you will get very bad ghosting due to the difference in time of the signal from the two transmitters. Even if they are on the exact same time (unlikey) the difference in distance will cause ghosting due to the time it take the signal to reach you.
We have this problem where we live on a mountain and can get signal from two low band VHF stations. Signals in this band travel further. We used to get a "venetian blind effect" on the picture and sometimes would get the sound from the wrong station.
The delay was about a second except in summer when daylight saving differences between the two states where the transmitters were located put them an hour and a second apart.
I built a custom antenna with a very strong front to back ratio to reject the rear signal.