$N>3$ then by a theorem of Bass [@Bass] there are many non-trivial linear relations (regarded as *seeds*) in $\MPV(1,N)$ whose structure is clear to us. Multiplied by MPVs of weight $w-1$ these relations can produce non-trivial linear relations among MPVs of weight $w$ which we call the *seeded relations.* Similar to these relations we may produce new relations by multiplying MPVs on RDS of lower weights. We call such relations *lifted relations*. We conjecture that when level $N=3$ all linear relations among MPVs are consequences of the RDS and the lifted RDS with $d(w,3)=2^w$.

Among MPVs we know that there are the so-called finite distribution relations (FDT). Racinet [@Rac] considers further the regularization of these relations by regarding MPVs as the coefficients of some group-like element in a suitably defined pro-Lie-algebra of motivic origin. Our computation shows that the regularized distribution relations (RDT) do contribute to new relations not covered by RDS and FDT. But they are not enough yet to produce all the lifted RDS.

We call a $\Q$-linear relation between MPVs *standard* if it can be produced by combinations of the following four families of relations: regularized double shuffle relations (RDS), regularized distribution relations (RDT), seeded relations, and 