I can't seem to find the answer in the reading and don't remember answering this in class. This is possible. In fact, there is a limited amount of secondary growth that does occur in some monocot stems. But it isn't organized to leave concentric rings of secondary xylem and phloem as occurs in dicots. Not all palms do get big in diameter.
Some species stay small, and some individuals of species that can be big are stunted individuals.
Leaf bases accumulate and make up some of what appears as the stem, even though they aren't really stem at all. The central axis that joins the leaflets of a compound leaf together is referred to as a rachis. If the leaves are attached to petioles, and the thing in the middle isn't attached to any leaves, what in the hay is it. Also, are we going to get to hierarchy and evolution within the PNW forest, angiosperm vs. gymnosperm. I've seen some pretty puny palm seeds that grow into pretty big plants.