It is well known how to produce a NIZK that curvepoints $aG$ and $aP$ have the same discrete logarithm $a$ with respect to the curvepoints they are multiplied by. There is also a way to prove that a curve point $aG$ has the same discrete logarithm as one of $b_1P$, ..., $b_nP$. I think this is due to Cramer but I first encountered it in Traceable Ring Signatures.
My question is: is there a threshold version of this? That is, given a set of $M$ discrete logarithms, can I prove that I know $N$ of them?