Only 3-4 flavors of B&J ice cream are CY. (I think under Belz.) The rest are under the OU, if I recall correctly, and state that they are not CY.
As far as I’m aware it is illegal to add anything other than cows milk to milk in the US and hence the basis for Rav Moshe’s heter for “chalav company”, which is generally referred to as chalav stam. (On the other hand, even according to Rav Moshe, it is assur to buy unsupervised milk directly for a farmer.)