According to Plato the soul has three aspects or parts. Does Plato put forward good arguments in support of this tripartition?

In Book 4, Plato gives us an account of the sou and he delves into this again in books 8 and 9, but for the purpose of this essay I shall focus on book 4 as it is here we get the most substantial argument for the tripartition of the soul. Hi argument is based on a number of premises; namely that the same thing cannot be characterized in the same respect, in relation to the same thing at the same time, and as we have evidence of internal conflict in human deduces that there must be multiple parts in the soul. However, Plato goes on to presuppositions about the number and nature of these parts. Thus in this argument I shall be exploring the ways in which Plato fails to give an adequate argument for his tripartion in book 4 of the republic.
Let us begin at the beginning of Plato’s argument in Book 4 and his first claim that the same thing can not be characterized in the same respect, in relation to the same thing at the same time. He shows us that there is evidence of internal conflicts between motivations within humans such as the thirsty man who has an aversion to drink(439). He has here successfully shown that there is a part of the soul that desires basic needs such as food and drink (noting the correlative relationship between an unqualified basic desire and an unqualified basic object, and a more specific qualified desire and specific qualified object), and another part that has the capacity to oppose this basic desire. The problem here is that he has made no account for the fact that there are clear instances where it seems that there are conflicting desires which spring from only one of the Platonic parts; namely the appetitive. Although he has specified that he is talking about basic (unqualified) desires he makes no attempt to limit the types of desires that the appetitive part may pursue. Thus, he is left open to criticism, and some such as Hendrik Lorenz comment that more ‘refined’ desires may develop, such as a desire for wealth. In these situations, it seems certain that there can be conflicts within the appetitive part alone; for example in the cases of some mental disorders such as anorexia or bulimia – a persons desire for food is in conflict with their desire to be thin. There are serious implications if we accept the possibility of refined desires: Plato takes conflict between desires as a basis for proving the partition of the soul, but in acknowledging the possibility of the appetitive part conflicting with itself means acknowledging subdivisions of the appetitive part, which then refutes the tripartite soul as there would be no need to look for an outside source of conflict.
Another striking problem arises from his description of appetitive part in concerns to its place in the soul’s hierarchy. Socrates claims that the appetite is the lowest and irrational part of the soul (439d7), and so it needs to be governed by the other parts (4426/7). However, what type of rationality is Socrates talking about? For it seems that the appetitive part cannot be wholly irrational, as shown in its capacity for means-end reasoning: we drink to not be thirsty, we desire food to not be hungry. The mere fact that the appetite is able to direct us in things that are of imperative importance to our health suggests an intrinsic element of rationality and reason. If this true then what is the need to differentiate between this element of the soul and that of reason? Furthermore in the Republic Socrates seems to treat desires such a thirst and hunger as desires that are independent of reason, not only again suggesting the appetitive part has some basic rationality of what is good for the person, but it also throwing the argument Plato’s argument in Book 4 into a questionable light, for in stating this he contradicts the Socratic idea about the motivation of good merely, it may be argued, to