It is not very common, but possible
(for clarity's sake I'll assume C-Major and use roman numerals for chords, and scale degree numbers and names for notes)
Doubling a chord's third
Generally. in polyphonic music and especially in four-part writing, we avoid doubling the mediant in a tonic chord. That is because doing so would alter the chord's character, and make it sound more like the iii. We usually only double the third of the I when resolving the vii6, but that's for another question.
On the other hand, doubling the third of the ii (namely, the subdominant), makes it more like the IV, which is often desirable, and also makes for a smoother voice-leading.
A problem with your requested voice leading: I tends to iii
In a typical voice leading of your example, the dominant chord's seventh would to resolve to the third of the I, as well as its fifth. So F->E, and D->E, or 4->3 and 2->3. This means a doubling of the mediant. Here, the dominant's seventh also functions as an upper leading-tone, which in conjunction with the former would lead to further altering the character of the I towards that of the iii.
A possible Solution: An irregular resolution of the dominant's seventh (but not really)
This troubling situation can be remedied by stepwise motion of the subdominant note. A E->F->G procession of the voice is preferrable for two reasons.
- It's contrapuntally agreeable as a stepwise occurring dissonance.
- It avoids the doubling of the mediant
- The movement by thirds between the bass and the voice containing the 4 means it's now technically not a seventh. It only dissonates in relation to the leading tone, (a tritone relation).
For all of these reasons, it's okay not to resolve the 4 to the 3 in this example, since its downwards resolution is usually required in the context of a 7-6 dissonance.
The V43 chord is quite common in the Classical era but - in my experience - the vii6 is more commonly used instead in the Baroque era.