We suggested that periphrastic do, modal auxiliaries and auxiliary have and be can be residents of INFL [+Tense].
However, the syntactic behaviour of auxiliary have and be differs from that of the other elements. There is syntactic evidence suggesting that have and be are not base-generated in INFL, but in V°. Have and be are assumed to be the head of a separate VP, and they move to INFL whenever this position is not filled by a modal auxiliary.
Despite the differences outlined above, we will continue to treat have and be as analogous to modal auxiliaries and periphrastic do (i.e. as base-generated under INFL), since we want to keep our tree diagrams as simple as possible. For more details on the differentiation between auxiliary have and be and modal auxiliaries / periphrastic do read the links below.