First off, I question whether you are actually working with fully decoded PCM data values. If you are directly adding bytes, that would only make sense if the sound was recorded at 8-bit resolution, which is done less and less. These days, audio is recorded more commonly as 16-bit values, or more. I think there are some situations that don't require as much frequency content, but with current systems, the cpu savings aren't as critical so people opt to keep at least "CD Quality" (16-bit resolution, stereo, 41000 fps).
So step one, you have to make sure that you are properly converting the byte streams to valid PCM. For example, if 16-bit encoding, the two bytes have to be appended in the correct order (may be either big-endian or little-endian), and the resulting value used.
Once that is properly handled, it is usually sufficient to simply add the values and maybe impose a min and max filter to ensure the signal doesn't go beyond the defined range. I can think of two reasons why this works: (a) audio is usually recorded at a low enough volume that summing will not cause overflow, (b) the signals are random enough, with both positive and negative values, that moments where all the contributors line up in either the positive or negative direction are rare and short-lived.
Using a min and max will "clip" the signals, and can introduce some audible distortion, but it is a much less horrible sound than overflow! If your sources are routinely hitting the min and max, you can simply multiply a volume factor (within the range 0 to 1) to one or more of the contributing signals as a whole, to bring the audio values down.
For 16-bit data, it works to perform operations directly on the signed integers that result from appending the two bytes together (-32768 to 32767). But it is a more common practice to "normalize" the values, i.e., convert the 16-bit integers to floats ranging from -1 to 1, perform operations at that level, and then convert back to integers in the range -32768 to 32767 and break those integers into byte pairs.
There is a free book on digital signal processing that is well worth reading: Steven Smith's "The Scientists and Engineers Guide to Digital Signal Processing." It will give much more detail and background.