  We study the equational theories and bases of meets and joins of several
varieties of plactic-like monoids. Using those results, we construct
sublattices of the lattice of varieties of monoids, generated by said
varieties. We calculate the axiomatic ranks of their elements, obtain
plactic-like congruences whose corresponding factor monoids generate varieties
in the lattice, and determine which varieties are joins of the variety of
commutative monoids and a finitely generated variety. We also show that the
hyposylvester and metasylvester monoids generate the same variety as the
sylvester monoid.
