In an earlier paper, the authors showed that standard semigroups ${𝐌}_1$, ${𝐌}_2$ and ${𝐌}_3$ play an important role in the classification of weaker versions of alg-universality of semigroup varieties. This paper shows that quasivarieties generated by ${𝐌}_2$ and ${𝐌}_3$ are neither relatively alg-universal nor $Q$-universal, while there do exist finite semigroups ${𝐒}_2$ and ${𝐒}_3$ generating the same semigroup variety as ${𝐌}_2$ and ${𝐌}_3$ respectively and the quasivarieties generated by ${𝐒}_2$ and/or ${𝐒}_3$ are quasivar-relatively $ff$-alg-universal and $Q$-universal...