Co-managed IT
An arrangement where an outside provider works alongside internal IT staff rather than replacing them.
Co-managed usually means the internal person keeps the relationships, the context and the projects, while the provider takes the volume: the tickets, the patching, the after-hours cover, or whichever part is drowning them.
It is common at around fifty people and up, where there is one IT person who cannot cover holiday, illness or the whole surface area alone.
Below that, the equivalent is usually not co-managed IT but freeing whoever has inherited IT as a side job. Same shape, smaller scale: they keep the context, the provider takes the password resets.
What it costs
Priced the same per user as fully managed in most cases, since the ticket volume rather than the org chart drives the cost.
Related questions
Is co-managed cheaper than fully managed?
Usually not per user, because the cost is driven by ticket volume rather than by who else works there. The saving is in what your internal person is freed to do.