Found this post via Google, and thought I'd provide an expanded list of options for achieving this result from another article on the topic. Depending on your use case, here are a different approach that will add a vertex or, in some cases, add multiple. Admittedly, some are better suited than others. All use the Editable Poly modifier's tool set.
1. Insert Vertex Tool
In edge mode, there's a button labeled
Insert Vertex. It does just what it says. Just click on an edge to add as many vertices as you want. Enable snaps (midpoint ideally) to avoid going crazy.
2. Connect Tool
Click any two edges while in edge mode and you can use the
Connect tool. This creates an extra edge between the two (or more) selected edges. There's a new vertex at each endpoint.
3. Quick Slice
Quick slice will create an edge on a two-dimensional plane (or 3D plane if in a non-projected view) that creates a new vertex point at each intersecting point with another edge on your model. Not an approach I'd use but would certainly create extra vertices.
4. Slice Plane
Similar to the quick slice tool but lets you use the gizmo tool to adjust in 3D space from a 2D view. Creates many vertices at intersection points.
5. Tesselate Tool
Again, not an approach I'd recommend but can be useful in some cases. Essential subdivides your geometry by adding extra edges. Will be restricted to whatever sub-object selection is made (face or edges). New vertices are at the endpoints.
Source (has pictures): https://www.rendernode.com/ways-to-add-vertices-in-3ds-max/