Which verbs apart from the pure copula follow the existential 'there'?

The existential 'there' is usually followed by a form of the verb 'to be', used as a pure copula.

For instance, rather than saying, a wrench is on the bench, you'd say there's a wrench on the bench.

Biber, Conrad and Leech (2002) list a number of syncategorematic/copular verbs which can also follow the existential 'there', eg:

There used to be a house ... there's supposed to be a plot ... there seems to have been a mistake ... there's said to be a ghost ...

They don't make a distinction which I've noticed about what I call 'emergent-type' verbs, always used in the past, describing, as I see it, an action which has emerged, but seems as yet incomplete, eg:

...there arose such as clatter ... there appeared a great multitude ... there emerged, out of the freshly tilled soil, ...

I noticed today another type which I hadn't clocked before ... the use of the intransitive after 'Once upon a time', eg:

Once upon a time, there lived ...

I can't think of an instance where you'd use a transitive verb in this construction.

Are there any other types of verbs that can follow the existential 'there' in declarative sentences that you know of that I can add to my list?

You might be interested in the related topic of the presentational construction.

In form, the presentational construction uses the dummy pronoun "there" as subject but some other verb than BE as the main verb. E.g. "There remain only two further issues to discuss"; "There seems little doubt that the fire was started deliberately."

Some verbs (and verbal idioms) in this construction are: appear, arise, arrive, develop, emerge, enter, escape, follow, grow, lie, live, loom, occur, persist, sit, spring up, sprout, stand. Many of these verbs have to do with being in a position or coming into view.

Most presentational clauses are of the bare type or have a locative extension. (But there are exceptions, e.g. "There remain only two further issues to discuss."; "There remained only two officers alive.)

There are some differences in pragmatic constraints between presentationals and existentials. One difference is that definite noun phrases occur more readily as the "displaced subject" in presentationals than in existentials.

Note: The info and examples in my post are borrowed from the 2002 reference grammar by Huddleston and Pullum et al., The Cambridge Grammar of the English Language, pages 1402-3.