Thanks for a tip with mirror=none. I learn more and more about snap data 
About the problem "body + head", both constructed from halves:
I checked Beta1b snap data and it works well for body+head combinations but you can see the problem with, for example, a horse head and horse head armor - see the attached picture (test.png).
mirror=none does not help here, I believe, because we cannot know which half (left or right) is "primary" for each part and which one is "mirrored". My idea is to use caps parameter. If mirroring of SNAP_CYL works correctly and mirrors "caps" direction as well, it should work. Do you agree?
I made a schema for better understanding, see the second picture (schema.png), please.
About the problem "body + head", both constructed from halves:
I checked Beta1b snap data and it works well for body+head combinations but you can see the problem with, for example, a horse head and horse head armor - see the attached picture (test.png).
mirror=none does not help here, I believe, because we cannot know which half (left or right) is "primary" for each part and which one is "mirrored". My idea is to use caps parameter. If mirroring of SNAP_CYL works correctly and mirrors "caps" direction as well, it should work. Do you agree?
I made a schema for better understanding, see the second picture (schema.png), please.