Does anyone happen to know of any geospatial indexing solutions that can also index simultaneously by other dimensions. Temporal indexing for example (not only where, but when)?
As a practical matter, you want to fit the indexing structure to the properties of your data model as closely as possible. Increasing the generality of high-dimensionality spatial indexes comes at a high cognitive cost, so most complex high-dimensionality indexes are bespoke designs to limit generality. Things become pretty messy when you mix dimension types that are interval-like (e.g. polygons) and monotonic-like (e.g. temporal) so almost no one does it.
You can build, say, a general 8-dimensional index that can handle (some) distributions of interval and monotonic types simultaneously, in addition to the usual boring data types, that has excellent performance and scalability characteristics. It would probably only require something like 1000 lines of C++, so not too onerous. However, the code logic would be nearly impenetrable to read, never mind write, which matters for practical engineering.