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They do stack, just have to be different spirits. I run, stag, owl and boar, each increase movement speed, skill speed, and each adds 20% to a elemental damage (boar is fire, owl is cold and stag is electric.
When I kill a rare my dps panel sky rockets and I have summoned 2 out of three spirits at the same time. I run a trinity build thus the need to try and keep my elemental damage in relative sync. Unfortunately I can't use a head hunter belt as I need to use ingenuity (old school) to max my resistances.
They literally do not work this way. You are fake news.