Some beam combining is just lens squeezing a bunch of side by side lasers down into a smaller beam, where the beam shape doesn't matter as much as beam power.
The easiest way to combine two beams right on top of each other is just for them to have orthogonal polarizations, and run them "backwards" through one of the various optics that can split polarizations. You then end up with an unpolarized beam. With a little more care, if you can make sure the phases of the two beams are the same, you can combine two orthogonal linear polarized beams and end up with a linear beam output at 45 degrees to the original polarization, which then allows you to repeat the combining process. You can also use diffraction gratings to combine several beams on to one output beam, without using polarization.
Doing these methods in a coherent fashion requires careful control of the relative phase of each laser, and starts acting more like phased arrays from radio/microwave bands. Things also get messy, as you can easily get into situations where ray optics no longer work and need to work with quasioptics.
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