BWS 2001 and the 2001 WBF Standard Card both describe 1M-P-3M-P-(3M+1) as a shortness-asking relay. Some notes I found on line describe 1M-P-4♦("super limit raise")-4OM as a shortness-asking relay as well. I have assumed from discussions with my regular partner and mentor that 1M-P-4M-P-relay would also be a shortness asking bid. Apparently, however, there is not literature on this.
However, because of a debate on Bridge Base Forums, I checked with Eric Kokish about this sequence. I thought I would share his view, to perhaps get this issue "in print."
His view was that random cuebidding in this sequence is an inferior (but majority) position, majority because of laziness in theory application (I agree). The far better approach, he noted, is that of the minority who view the relay as in fact a shortness asking bid. A frequent corollary to this agreement is to have Opener's other calls (perhaps using 4NT as the for the other-major stiff) show Opener's shortness, allowing Opener to either ask for shortness or show shortness as tactics necessitate.
Do what you will with this information.