Can the application process for switching from a UK Tier 2 ICT Short-term multiple entry visa to a UK Tier 2 ICT Long-term multiple entry visa be carried out in the United Kingdom? Or will the visa need to be processed from the home country? The applicants will continue to work for the same employer as mentioned in the short-term visa application. The official webpage explicitly says that holders of multiple entry work permits are not eligible for the same, but I think I might be misunderstanding.
All the current Tier 2 ICT work permit categories allow one to leave and reenter the UK, but this doesn't make them Multiple Entry Work Permits. A Multiple Entry Work Permit is (or was?) instead granted to workers who live and primarily work outside the UK but are required by their employer to come to the UK periodically to work for short periods, kind of like a visitor visa for a worker. The best description I could find is this third-party document. The fact that I can't find a mention of this in the current immigration rules may mean that it no longer exists and the reference is obsolete (or I am blind).
In any case, if the ICT Short-term work permits they have allow the workers to bring dependents and accrue presence for ILR then those are not Multiple Entry Work Permits and they may apply for leave to remain as ICT Long Term workers while in the UK in their current status. The immigration rule corresponding to that text is 245GD(b)(i)(4).