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Hello, can a thousand son caracter go Under 3++ with a temporare buff is the limitation from the mark for the army building?

I say yes as the buff is not from the mark

" Models with a mark of tzeentch have +1 to their invulnerable save (to a maximum of 3+)."
I would say no, that's the limit.

Could argue you could hit 2++ if you didn't count the mark of tzeentch at all.

FAQ on some previous "bonus on benefit x to a maximum of y" says that the maximum of y is hard-capped.

No matter what sources you gain the benefit from, having the item or special rule with a capped roll+ overrides all other sources and bonuses.

 Kommissar Kel wrote:
FAQ on some previous "bonus on benefit x to a maximum of y" says that the maximum of y is hard-capped.

No matter what sources you gain the benefit from, having the item or special rule with a capped roll+ overrides all other sources and bonuses.

And those lesser bonuses can counter lesser deficits that would otherwise leave the cap not reached. This is not likely to happen with Invulnerable Saves ( since I do not know of a rule that reduces Invul Saves), but it is demonstrable with Reanimation Protocols, Crypteks, Decurion and Instant Death.

Death Hex and the loyalist equivalent reduces invulnerable saves by 2.