What are these Auxiliary-like verbs?
Solution 1:
Verbs such as continue, stop, beg, tell that can combine with other verbs are called catenative verbs. The Oxford Dictionary of English Grammar (p59) has this entry on catenative verbs:
A verb that can form a chain with one or more subsequent verbs, e.g.
- want to go
- hate to tell you
- begin walking
- go shopping.
The construction may involve a direct object, e.g.
- She wanted them to go
- He made us laugh
- I watched him paint/painting the door.
The Cambridge Grammar of the English Language (p1177) points out the recursive nature of catenative verbs:
The term 'catenative' applies to a large class of constructions where a verb has a non-finite internal complement. The name reflects the fact that the construction can be repeated recursively, yielding a concatenation ('chain') of verbs.
i. I wanted to arrange for Kim to do it.
ii. She intends to try to persuade him to help her redecorate her flat.
Later in the CGEL (p1206-1220) there is a lengthy section that proposes the re-analysis of auxiliaries as catenatives:
... the position taken here is that there are nevertheless compelling grounds for preferring an analysis of the modal, tense, aspectual and voice auxiliaries as catenative verbs taking non-finite complementation.
The CGEL approach is called the "catenative-auxiliary analysis" in contrast to the traditional "dependent-auxiliary analysis.