I cannot help but question the validity of the Aristotelian idea of the forms. While it seems that form exist objectively, the forms that we see in the world appear to be artificial concepts, means by which similar things are grouped.
By convention an shape consisting of 3 sides is called a triangle. Instead of grouping all such objects under one form we could have separate names for each different type of triangle. A right triangle an isosceles triangle etc. are all grouped under triangle but only due to accidental convention and each type could have its own form instead being labeled triangular.
Consider also that forms tend to be fuzzy sets. There is no hard and fast rules with regards to were an object stops being one imperfect actualization of one form and becomes another. Take for example the instrument known as a triangle. It is a metal bar bent into the shape of a triangle. It has the form of triangularity. It is not perfect, the corners are rounded and one corner is missing. But say we start bending the triangle very slightly. Since it is never the perfect actualization of triangularity we can say that even slightly bent, it contains the form of triangularity. At what point in bending the triangle does it cease to have triangularity and instead takes on a different form? This is subjective and different people can disagree.
Since language is finite, it is necessary that similar items are grouped under the same form. But when items that are clearly under one form begin to change, like the triangle, they start to fall out of the group they were placed in. As I stated, form are fuzzy sets, meaning that there can be overlaps and while the sets are objectively defined, the overlaps have to be placed subjectively because they do not clearly belong in one set more then another.
If forms are only creations of the intellect that were developed as languages were created, then when we recognize an object for the form it actualizes, the form itself does not exist in our mind. Only an object that actualizes the form, as defined, contains that form. As such, the claim that the soul or the intellect is immaterial because the forms exist within is not true. The intellect does not possess the form of the object within it.