Terminology varies, so the answer to this question depends on how precise one would like to be when using the term 'object'.
One view would hold that anything following a verb that is specifically allowed by that verb (and verbs like it) should be classified as an object. In this view all of the following might be referred to as objects.
She started [buying novelty mugs].
She said [that I should get a new hat].
She got [me] [to go along with it].
She put [the hat] [on her head].
She saw [me] [leave the restaurant].
You will notice that all of the above seem to be different types of 'objects' and, for the most part, are not interchangeable. The reason for this is their internal structure - they are not the same type of word, phrase, or clause.
Thus, an alternate view holds that all of the above are not 'objects', but simply 'complements' of the verb - elements that are allowed by the verb (and verbs like it), and that 'objects' are only NPs. According to this view, verbs should then be classified into categories like:
monotransitive: allows a single complement in the form of an object NP
She failed [the test].
ditransitive: allows two complements in the form of object NPs
She brought [the boys] [a sandwich].
prepositional: allow complement(s) in the form of prepositional phrases (possibly in addition to a complement in the form of an object NP)
He talked [about it].
He told [me] [about it].
He talked [to me] [about it].
catenative: allow a complement in the form of a non-finite clause (with sub-classes for those allowing -ing clauses, plain infinitivals, to-infinitivals, past participials, and those that allow an NP to precede these)
She can [do the dishes].
She helped [me] [do the dishes].
She was [thinking about it].
She got [me] [thinking about it].
She was [taken out of the game].
She had [me] [taken out of the game].
She started [to like it].
She convinced [me] [to like it].
reporting: allow a complement in the form of finite subordinate clause (with sub-classes declarative, interrogative, exclamative, subjunctive, and those that allow an NP to precede these)
He answered [that he didn't want to go].
He told [me] [that he didn't want to go].
He wondered [whether we wanted to go].
He asked [us] [whether we wanted to go].
He saw [what a mess it had become].
He informed [me] [what a mess it had become].
He recommended [she take the day off].
While it is true that many verbs allow more than one of the above patterns of complementation, this view holds that there is no reason to lump all of the bracketed expressions above into a single category 'object', as this does not allow us to accurately describe what is or is not allowed in a clause headed by a particular verb.
The solution is to use the more general 'complement', meaning an item allowed by the head word or phrase, and then create various categories of 'complement' to describe what items are allowed by particular verbs.
Whatever terminology is used, one thing is certain: an accurate description must include the form (internal structure) of the item(s) found along with a particular type of verb and not with others.
