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.