A. She is likely/sure/certain to start her new project.
She may start her new project.
Are the senses and the roles of the to inf. the same as 'start her new project' of 'may', complementing the (modal) verbs and indicating the action of the subject? Do we speak them in the same sense? If we classify the main verb of modal verbs ad the complement of the modal verbs, do we also classify the inf. above as the complements of the 'be + adj.'s? Or is the to-inf. just an object?
B. I'm dying/willing/curious/anxious/eager to eat that cake.
I'm dying/willing/curious/anxious/eager for that cake.
Do we speak the to inf.s above in the same sense as the 'for~'s? Do they mean the same, expressing the subject's wish, desire, or plan as adverbials?
C. I hoped for some money./I hoped to take the train.
I begged for more candy./I begged to go to the movies.
I longed for an A./I long to get an A.
I volunteered for the job./I volunteered to help the kids.
I was aiming for the trophy./I was aiming to receive the trophy.
Do these to inf. express desire/intention as adverbials, same as the 'for+N's? Or, are they just objects?