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Inviting 2M

Bidding after 2M implies invitational+ since 2M is already an appealing contract.

1♣ - 1M -
2M -
2NT!INV+, no longer side suits
3♣♦INV, 5+#
3M!LIM, (4333)
3NTCOG, (4333)
4♣♦!S/T SPL, 0–1#

As the highest step of invitation, 3M should be very specific. I choose (4333) to enable choice of games between 3NT and 4M.

Why bother bidding another suit to 2M? It helps finding double fits.

1♣ - 1♥ -
2♥ -
2♠INV, 4+♠, 5+♥
3♠!S/T SPL, 0–1#
1♣ - 1♠ -
2♠ -
3♥INV, 4+♥, 5+♠
4♥!S/T SPL, 0–1#