It seems that the term multi-sourcing is actually being called single-sourcing in some quarters.
Multi-sourcing in IT, from what I understand, is having multiple suppliers providing services.
Traditionally these suppliers would be managed separately, which was one of the downsides of an otherwise logical means of getting value for money. These days many contracts are multi-sourced with one supplier in charge of managing all the other suppliers. T-Systems' deal with BP springs to mind.
But I had a meeting last week with someone involved in putting together these multi-sourcing contracts. He said to me that this type of contract, where there are multiple suppliers and one of them manages the others, is now referred to as single sourcing because one company is responsible.
Confused? If so here is a article that might help you navigate the multisourcing contract minefield. Free advice from lawyers.
See how BP makes multi-sourcing work here.