In regard to metaphysics, there are only three axiomatic concepts - Existence, Identity, and Consciousness. These three are often differentiated from the general usage of the term axiom, by referring to them as the basic axioms. Technically, Causality is a corollary of the axiomatic concept - Identity.
Volition, the validity of the senses, entity, and the self - are epistemological axiomatic concepts in the sense that they are self-evident, primaries in regard to any given instance of cognition/conceptualization. However, since metapysics is more fundamental than epistemology, these epistemological axiomatic concepts are, more precisely, corollaries of the three metaphysical axiomatic concepts; specifically, corollaries of the axiomatic concept -Consciousness.
Informally, corollaries can and often are referred to as 'axiomatic concepts' and/or 'axioms', however with the understanding that they are not a basic axiom. Also, keep in mind, that an axiomatic concept is not synonymous with axiom; An axiom is a statement that identifies an axiomatic concept in explicit, propositional form. Again, however, you will probably find examples of the two being used interchangeably either erroneously, or more commonly as linguistic shorthand (it's easier to say axiom instead of axiomatic concept).
In regard to your question: Objectivism recognizes only 3 basic axioms - Existence, Consciousness, and Identity. in regard to the non-basic axioms (corollaries) those presented in the Objectivist literature are not considered exclusive.