Is it possible to combine independent digital TV antennas?
The electromagnetic wave and antenna don't know if the TV is analog or digital. To them, it's the same! This means that most of analog transmission experience applies to digital TV as well. 

So in general, you should point the antennas correctly for best signal quality and use proper polarization as well. 

You can use multiple antennas for best signal quality, but there are some bad sides to that as well. Let's say you have an antenna correctly set up for one signal source. It is designed for its frequency, has sufficient gain and is correctly pointed at the signal source. That antenna will still pick up signals from other sources as well, but they will be weaker. If you have another antenna matched to the weak signal source of the first antenna and you combine them both directly, first antenna's weak signals can interfere with second antenna's strong signals. Usual solution to that is to use a diplexer. It's a device that has a band pass filter (some implementations may just use low pass and high pass filters) and you set it up so that it passes through the frequencies which a particular antenna is receiving the best and blocks other signals. This way, at the output of diplexer you'll only have the best signals from all antennas you have and weak signal from one antenna won't interfere with a strong signal from another antenna. Of course, diplexers have their own insertion losses, so they'll decrease the signal quality. The idea is to use as few antennas as possible to get the best signal and to use diplexers sparingly in order to prevent their insertion losses from having a negative net effect on signal quality.

Some digital TV standards allow use of "auxiliary" broadcast locations so that you have one main transmitter and few smaller transmitters connected to the main transmitter. In such setups, the signals from the smaller transmitters shouldn't interfere with the signal from the more powerful transmitter. Unfortunately, I don't have any practical experience with this, so I won't go into any details.

The other important thing is the digital cliff and analog slope. In digital TV systems, as long as your signal quality isn't horrible, you'll get relatively good picture. Problems will occur once it gets borderline and then quickly after that, you'll completely lose signal. You can take advantage of that to have good picture quality even with not so good signal, but the downside is that you'll be more sensitive to bad weather than if you had good signal quality. On the other hand, in some situations setting up a proper TV antenna system can require expensive antennas, cables and expertize so exploiting the digital cliff effect can be economically justified.