Most of the time, no. There are a few exceptions though:
Special release dragons (Halloween, Holiday, and Valentine's Day) can only produce eggs of their own breed during their holiday season. During that period, they may produce multiple eggs.
Certain dragons have characteristics that limit how often they can breed. Celestial Dragons and Painted Ray Pygmies can only breed once every 28 days, so when they breed they may produce multiple eggs at once.