This auction can create some problems for the intervening side. A suggestion for dealing with them follows.
Assuming that 3 Diamonds was preemptive, which is how most partnerships play it, the best agreement is:
4♣️ = Majors. Over this bid, 4♦️ and 4♥️ are transfers to a major; 4♠️ is slamish with hearts (watch out!), and 4NT is slamish for spades. Note that 4♣️ over a double of 1♦️ can be quite weak, so these slamish auctions require really strong hands.
4♦️ = ♣️+Major. Over this bid, 4♥️ is pass/correct, 4♠️ is pass/correct, 4NT is slamish for ♣️ and 5♦️ is slamish with both majors)
4♥️ = To Play, not Strong
4♠️ = To Play, not Strong
X = Takeout (never short in a major), or any strong hand. Now, 4♣️ asks: 4♦️ Normal takeout, 4M = 6+M Strong, 4NT 6+♣️ Strong + ♦️control, 5♣️ 6+♣️ Strong, no ♦️ control. If partner doubled 1♦️ and now, instead of bidding 4♣️, bids 4♦️, he has both majors and wants you to pick one of them.
The clear advantage of this sequence can be observed with a hand such as this:
xx AKJxx xxx KQx
(1♦️) X (3♦️)
You can now show both your hearts and your strength, informing partner that slam is possible. You start by doubling, and later bid hearts. Your partner will know you have a good hand with 5+♥️, an important information when deciding his next bid.