They stack. I did some testing, which will be a bit long here, but this is what I have got:
I went with my level 101 Mechanic. His stats are:
Str: 90
Agi: 57
Vit: 36
Int: 30
Dex: 66
Luk: 30
I wore +9 Temp Str Boots with FS7, and avoided any procs. I tested on Lunatics as they are neutral, and easy to find. I made all hits with Maximize Power on to try to eliminate as much variation as possible. I used two completely unupgraded Crimson Two Handed Axes, with no cards. One wind, one fire. The results are:
Wind axe + Supp. Part Con + 2x Arq. Necklace : 5646
Wind axe + 2x Arq. Necklace : 4908
Wind axe + Supp Part Con : 3696
Wind axe + Supp Part Con + 1x Arq Necklace : 4668
Wind axe + 1x Arq. Necklace : 3930
Wind axe only : 2952
Fire axe + Supp. Part Con + 2x Arq. Necklace : 4512
Fire axe + 2x Arq. Necklace : 3924
Fire axe + Supp Part Con : 2952
Fire axe + Supp Part Con + 1x Arq Necklace : 3732
Fire axe + 1x Arq. Necklace : 3144
Fire axe only : 2364
Effect of wind element: 25% extra at all points
Effect of Supplement Part Con: +15% with both necks, +18% with only one neck, and +25% with no necks.
Effect of one necklace: +26% with Supp Con, +33% with no Supp Con
Effect of two necklaces: +53% with Supp Con, +66% with no Supp Con
When comparing against completely base values (axe only, no other gear as the base):
Axe alone = 100% damage
Axe + Supp Con + 2x necklace = 191% damage
Axe + 2x necklace = 166%
Axe + Supp Con = 125%
Axe + 1x necklace = 133%
Wind axe with all gear compared to fire axe with no gear = 239%
So, the necklaces stack additively, both with themselves and with Supplement Part Con, but multiplicative with the wind weapon bonus.
Edited by Latsabb, 21 May 2017 - 09:40 AM.