I believe Chaos rising is an expansion, not stand alone. For that to happens in Saints Row 4 we will have to install SR:GOOH in the same folder as SR4 which will make a catastrophic mess. Since it's a stand alone, having SR4 is optional, so GOOH must have its own data (.bin or whatever) but when the two game united for the sake of your request both data will be overwritten. your modded customized_item will absolutely be gone.
See, that's why a game can't be a stand alone and an expansion at the same time.
But if you okay with the other way around, opening SR4 content from GOOH, that is absolutely possible and a lot of game already did that.