The only way it's going to happen is to try to bridge between the ideal, and as close as we have already. Which is Meredith Instruments corner cube reflectors, 22mm type, found on eBay last time I looked for any (or sourced from the Chinese firm that makes them, and they shouldn't have to be that big anyway, 1cm might be ideal)... But those aren't mirrored on the outside surfaces, so that would have to be done. I can't afford to, and no-one else seems to want to.
There was talk of a four-sided axicon but that's even worse, because it would have to be made from scratch, unlike the corner cube, and anyone can easily demonstrate that the beams from such an axicon cannot tesselate compactly into a fine beam as closely as a three-sided one anyway. People have argued that aligning it would be easier, but it's not true, as machining and aligning parts for a three-sided system with its odd angles is actually easy, I worked out a design where the mounts can easily be cut with 20° angles on a crude bandsaw and take two drilled holes, one threaded, and still be finely and easily adjusted with two movements per diode mount, and one fore/aft translation and rotation of the axicon itself.
Knife edging can set beams close together, but the more you do it, the more interesting (and unlikely) the mirror shapes become, if you're really going to fit more than about 3 beams together. I worked out that 3 very close-set beams can be done by using spare Medialas Widemove scan mirrors, I think I included an image of that layout somewhere in that thread or elsewhere here. To do it with mirrors you need several more points of rotation or translation combined than you do with the 3-sided axicon (means complex mounts!), but unless someone makes an axicon with 6 sides, or bores the axis of a 3-sided one for a 4th beam, there's no point in planning for them because no-one can surmount the cost and effort to do it.
Edit:
If the mirror were a simple curved-surface cone it could not work, as the beam divergence would be like a flame thrower. Actually more like a floodlight.