What I was imagining was either:
1. A two-part round, with the first part consisting of an AP round to "crack" the anti-beam plate armor, and then a second part consisting of a plasma charge to melt through the anti-kinetic mesh armor (and flash heat the target).
2. A sort of twin weapon, one barrel shooting AT to crack and the other barrel shooting beams to shoot through the cracks.
#1 seems far more feasible, but also seems like the rounds would be larger than the average small arms round
maybe an "in game" reason for heavier, shorter range weapons?
#2 seems needlessly complex, very possibly highly inefficient, but would look cool
which means it would probably be the official government program. ;)
I'm not really sure how traditional melee weapons would defeat this sort of layered armor. They would have to actually crack the plate, but the anti-kinetic mesh would defeat the bludgeoning effect of a strike. Assuming a weapon could crack the plate, it would also need an energy based element to defeat the mesh
unless we are saying that sufficient sharpness could overcome the anti-kinetic mesh, in which case a flechette round might be a possibility for ranged weapons.
Hmmm
maybe a sort of "mace" designed to crack the plate and then fire off an energy charge on impact? Melee would consist of big Crack! Boom! strikes.
At any rate, it would seem that a large caliber complex-round weapon for ranged and a high impact but energy/powered edge for melee would be the order of the day.