The usual split gives the MSP the work that benefits from tooling and scale — monitoring, patching, after-hours coverage, security operations — while internal staff keep the work that benefits from knowing the business: applications, projects, user relationships. That division is not a rule, but it is the one that most often survives contact with reality, because it plays to what each side is genuinely better at.
Clients ask for it for two reasons that pull in different directions. Some have an IT team that is stretched and needs capacity. Others have an IT person they trust and want to keep, but know that one person cannot cover holidays, nights or specialisms. The first is a capacity conversation; the second is a risk conversation, and they lead to different agreements.
The mistake providers make is pricing it as a discounted version of fully managed. It is a different service: fewer endpoints under exclusive control, more coordination overhead, and a client with the expertise to evaluate your work in detail. Priced as a discount, it usually loses money, and the loss is invisible until the coordination time is measured.