Wray describes money in a country as a pyramid. In "Modern Money Theory", Wray, pg 85. So from that alone, MMT does support the role of money issued by non-government entities. To see why, he continues on pg 86 with:Private financial liabilities are not only denominated in the government's money of account, but they also are, ultimately, convertible into the government's currency.
We can think of a pyramid of liabilities, with different layers according to the degree of separation from the central bank...The shape of the pyramid is instructive for two reasons. First, there is a hierarchical arrangement whereby liabilities issued by those higher in the pyramid are generally more acceptable...Second, the liabilities at each level typically leverage the liabilities at the higher levels.