I wonder if there are more other auxiliary verbs in addition to that 23 common verbs.
The idea of 23 of them is new to me, but googling provides the following list:
- will
- shall
- can
- would
- should
- could
- may
- might
- must
- do
- does
- did
- am
- is
- are
- was
- were
- be
- been
- have
- has
- had
- being
That list is incomplete, but arguably also over-long. We can provide a fuller list:
- be
- am,
- are,
- is,
- was,
- were,
- being,
- been,
- can,
- could,
- dare,
- do
- does,
- did,
- have
- has,
- had,
- having,
- may,
- might,
- must,
- mote,
- need,
- ought,
- had better,
- shall,
- should,
- will,
- would
- used to
Not all of them are used much as such in all dialects, and in particular mote is pretty much obsolete bar the expression "so mote it be" found in Freemasonry, Wicca and some other modern magical or religious practices influenced by one or both of those.
We could add on contractions, and have a few more in the list (lots more if we allow the very many different dialect contractions of some of them), but this list of 30 seems a reasonable attempt to fill out the 23.
However, most of those are different forms of the same word, so we could in fact shorten the list to:
- be (am, are, is, was, were, being),
- can,
- could,
- dare,
- do (does, did),
- have (has, had, having),
- may,
- might,
- must,
- mote
- need,
- ought,
- had better,
- shall,
- should,
- will,
- would
- used to
And indeed, there is a relationship between some of those still listed as separate, with e.g. could being the preterite of can even though when used as auxiliaries the preterite works differently with tenses than it does with other verbs. Still, we could still shorten the list further:
- be (am, are, is, was, were, being),
- can/could,
- dare,
- do (does, did),
- have (has, had, having),
- may/might,
- must/mote
- need,
- ought,
- had better,
- shall/should,
- will/would
- used to