everything else either should be completely outsourced
That can create a different sort of shadow IT problem.
Company decides to outsource the internal helpdesk. Instead of being operated by employees who have a commitment to the business, it's now run by people who are paid to close calls as quickly as possible and have script-driven responses ("Step 1: have you turned it off and on again?").
Doesn't take long for people to find that logging support calls isn't very helpful any more. Then someone says "Bob had that problem, ask him". Bob explains his solution, it works. His solution may not be correct, it might even make things worse, but soon Bob is the unofficial go-to person for that group. After a while every group has their "Bob", who get frustrated because their real work is suffering, but they try to do their best for their colleagues, not realising that they may actually be making things worse in the long run with kluges & workarounds (ever tried to update a Word document from someone who thinks they know how to format stuff correctly, and shared their tips with everyone?)
Meanwhile the calls to the official support desk fall, which the IT group uses as proof that the systems are working well but which in reality shows that things are totally broken.