In addition to the equal-area projections of the azimuthal, conic, and stereographic classes, there are also many pseudocylindrical projections which are equal-area.
However, there is still another kind of equal-area projection of which several examples exist. These projections are based on transformations similar to those used to create the Lagrange conformal projection and the Miller cylindrical projection.
And then there is the Dietrich-Kitada projection, which could be thought of as deriving from conventional projections like the Globular projection and the Van der Grinten IV projection. (My page on that projection is just getting started, and is unfinished.)