Putting auxiliary verbs in order. In the sentence Immigration figures may have been rising, the main verb rising follows three auxiliaries: may, have, and been. Together these auxiliaries and main verb make up a verb phrase.
As shown in the preceding chart, when two or more auxiliaries appear in a verb phrase, they must follow a particular order based on the type of auxiliary: (1) modal, (2) a form of have used to indicate a perfect tense, (3) a form of be used to indicate a progressive tense, and (4) a form of be used to indicate the passive voice. (Very few sentences include all four kinds of auxiliaries.)
Only one modal is permitted in a verb phrase.