Answer: Certainly you can - though as a general principle it's better to double one of the other notes if the chord is major.

Best choices for doubling in a major triad in order of desirability: root, 5th, 3rd.

If there's a seventh in the chord it should not be doubled - sevenths want to "resolve," and doing both of them would make parallel octaves, which is thought to reduce the independence of the voices. A similar problem arises for major thirds in a dominant chord, which would prefer to move by half step to the tonic.

Even Bach occasionally will double a major third, but you get the impression he didn't enjoy it.