Permitted at Level 2
I have always thought that in principle permitted bids at Level 2 should not be two way and should always specify at least one suit.
So Multi and Suction are not allowed.
But what about McKendrick?
It might be an invite or it might be a weak take-out. And if the latter the suit is not specified.
Yet somehow it doesn't feel as esoteric as the other two.
Comments
Stayman is another example of a multi-way bid (it might have hearts or might have spades), and it isn't explicitly permitted at level 2 either.
I think both Stayman and McKendrick (i.e. 1NT, 2!s = bad NT invite or to play 3!c or 3!d) fall under the general permission to play "any common English system" which determine what's legal as a response to an opening bid; McKendrick isn't universal, but it is fairly common, especially at the club level. "System" covers NT response systems in addition to suit-opening response systems.
The "calls under level 2 agreements should not be two-way" principle seems to apply specifically to overcalls in second seat and/or over 1NT (except for a strong 2NT overcall), and doesn't apply in other contexts (other contexts are either more or less permissive than this). For example, two-level openings are more restricted than that, and must either be short or long in the suit opened (they can't show length in a suit other than the suit opened, e.g. a 2NT opening showing both minors is illegal at level 2).