Can two of these radio controlled planes fly at once?

If there is a switch to change from one ch to another ch, then yes you can. If not, then you are doing many things at once, and need the extra channel to do them. You can still run 2 planes at the same time in the same place, just make sure they aren’t on the same operating freaquencies. Different crystals can be bought from you local hobby shop. 1 set for the bird, and another for the controller.
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On RC Aircraft, "2-Channel" refers to the number of servos that the Controller operates on the aircraft… normally the Rudder (left/right) and Elevators (up/down).

To operate TWO aircraft at the same time the CONTROLLERS need to be on seperate frequencies… this is often a matter of selection at purchase or can be changed at the flying park.

IF the controllers are on the SAME frequency, the plane will react to which ever signal is stronger… YOU could end up flying BOTH aircraft or neither !!

GOOD LUCK.
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mairiner 3 answered this correctly. you may want to consider going with a nitro gas powered plane, 5 channel. little more money but worth every penny.
References :
2 years of flying.