> I wondered if it was possible to tell BaseX (or to have it understand by
> itself) that it can cache and reuse the results of
>
>     /tei:TEI/tei:text/tei:body//tei:ELEM
>
> and only apply PREDICATE on the saved set of results.
>
> Is something like this available in BaseX?

No, I'm afraid (and I'm not sure how to easily realize this for
arbitrary requests). If performance is critical, and if you believe
nothing more can be done, you could still think about creating
additional index structures for your data and access these instead
(just as Fabrice motivated in his reply).

> Unfortunately all I
> got back was a "Unknown option 'CACHEQUERY'" error (with BaseX 8.2.1). Any
> idea why?

I now know why: Because it has recently been removed. All it did was
to cache results before returning them to the client instead of
streaming them. This option was only used for our GUI, but another
solution has now been found there.

I have updated our documentation. Thanks for the hint,
Christian