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Inviting 2M

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

1-1M 2M-MIN, 11–14, 4=M
2NT!INV+, no longer side suits
3INV, 5+#
3M!LIM, (4333)
3NTChoice of games, (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-MIN, 11–14, 4=
2INV, 4+, 5+
3!S/T SPL, 0–1#
1-1 2-MIN, 11–14, 4=
3INV, 4+, 5+
4!S/T SPL, 0–1#