Any process that increases the frequency, rate, or extent of metanephric cap mesenchymal cell proliferation. Metanephric cap mesenchymal cell proliferation is the multiplication or reproduction of metanephric cap mesenchymal cells, resulting in the expansion of the cell population. A metanephric cap mesenchymal cell is a mesenchymal cell that has condensed with other mesenchymal cells surrounding the ureteric bud tip.