It's odd that the medieval tradition of philosophy contains a longer list of interior senses than that found in the De Anima of Aristotle. Was it the case that Aristotle was not aware of these other powers? Or perhaps he talks about them and I have just overlooked it? No idea. But the medievals (St. Thomas comes to mind right away) make a good case for their existence in the soul, especially in the soul of animals.
These two powers are the memorative and the estimative. Their object is not any one of the proper sensibles, or even any of the common sensibles, but rather the sensible per accidens. Thomas calls them intentions. This word is a bit annoying, since the same word is often used to talk about what goes on in the mind, first intentions being our names/concepts of various things (dog, red, three) and second intentions being the names/concepts about the first intentions (genus, species, etc.). So not only do these intentions of the inner senses share a name with those of the intellect, but they even seem to be universal. St. Thomas and St. Albert do not teach that these are universal, but even call them particular intentions.
I haven't read their teaching on this for a little while, but these particular intentions are only for the sake of action. This sounds reasonable, for when we talk about instinct in animals, it is generally understood that we are only talking about a principle of their activity. The argument that animals have some power in addition to the imagination is simple: the sheep are not afraid of the wolf's color, but of the wolf.
Now in man, things become more difficult. What is called the estimative power in animals, is called the cogitative power in men. This is on account of its close association with the intellect. St. Albert will often mention both the cogitative power and the intellect together when discussing certain things, as though it would be inconvenient to separate the activity of the one from the other. Besides receiving intentions in men, it also serves as a kind of medium between out intellect and our actions. Since the intellect has as its object the universal, it is not of itself able to make a proposition about individual actions and must therefore mediate through a lower power that is seated in some organ.
That these intentions are ordered to action gives them some degree of particularity, but there still seems to be something universal about them. Perhaps I'm just abstracting with my intellect and therefore missing it? For example, the sheep seems to have a universal principle (avoid wolves) which is applied to a particular instance (avoid that wolf). It seems that it might be worth considering what is meant by "universal" when talking about things that aren't in the mind. For example, any given body is such that it inclines to every other body according to an inverse square law. Thus, one body has a certain disposition to all bodies--hence one might say this is "universal" in some sense. Universal, when said of things in the mind, usually just means "said of many" or "true of many".