I do this also. The advantage is that responder can show one minor or both. One minor goes through the relay (of course he usually passes 3NT), two minors bid 3NT directly. Another improvement, is that instead of responder bidding the minor in which he's interested he's interested ...
We do this :
3C : Muppet Stayman
3D/3H : Transfers
3S : Relay to 3NT
3NT : Minor Suit Stayman, forcing to 4NT or 5m.
4C : Gerber
4D : 5-5 majors
4H/4S : both minors, void in H/S.
After relaying to 3NT, responder usually passes, but can also show a minor suit. We ...
We play the opposite, 1D - 1M - 3D guarantees 3 card support, 1D - 1M - 2NT is the same hand except that it denies 3 card support.
After 1D - 1M - 2NT, responder can pass, correct to 3D (NF), or start showing stoppers up the line.
After 1D - 1M - 3D, responder can pass ...
My biggest concern about doubling with the second hand is the lack of quick tricks, I expect my partners to have 2 quick tricks for a direct seat double. Even so, I'd probably double anyway, but would not be happy if partner later doubled the opponents.