  We study the four plactic-like monoids that arise by taking the meets and
joins of stalactic and taiga congruences. We obtain the combinatorial objects
associated with the meet monoids, establishing Robinson-Schensted-like
correspondences and giving extraction and iterative insertion algorithms for
these objects. We then obtain results on the sizes of classes of words equal in
plactic-like monoids, show that some of these monoids are syntactic, and
characterise their equational theories.
