You probably already know the requirement for how ingredients are listed on labels, from highest percentage to lowest, with some exceptions toward the end of the listing. As you are in the US, if you are not familiar with the requirements see this link. Knowing that, can help you to determine at least, the predominance of some of the particular oils in the soaps you like.
So if the above list is in the correct order, then there would be more goat milk than the oils coming after. But also if one ingredient is listed after another, they can also be equal in proportion. You can't always tell from the label what the actual percentage is, just that toward the top of the label it's more and toward the bottom it's less.
Another thought is that in some cases, other additives could play a part in how it feels on the skin. For example, corn silk, clay and other things like that can produce a different feel. So if anything other than oils are listed, that would be important as well if you are after the same type of feel on your skin.
So if the above list is in the correct order, then there would be more goat milk than the oils coming after. But also if one ingredient is listed after another, they can also be equal in proportion. You can't always tell from the label what the actual percentage is, just that toward the top of the label it's more and toward the bottom it's less.
Another thought is that in some cases, other additives could play a part in how it feels on the skin. For example, corn silk, clay and other things like that can produce a different feel. So if anything other than oils are listed, that would be important as well if you are after the same type of feel on your skin.