Supersonic V/STOL is possible, but not very practical. Any jet design is a comromise, and V/STOL even much more so. So why it might seem logical to "want" Mach 2 in your design, getting there is quite tough and will come at a cost. The P1154 was to have a complex engine with plenum chamber burning (basically afterburners on the "cold" front nozzles). Other higher speed V/STOL designs were to use multiple engines, or lift engines and other complex arrangements. All of these lead to extra weight, compexity, cost and high fuel consumption. When it comes down to it, most have concluded that they do no "need" MACH 2, especially with the costs/compromises it brings, and you do not need MACH 2 for close air support. If you really need a MACH 2 interceptor, better to have a conventional (non-V/STOL) design.
As proven with the Harrier, the best arrangement for a V/STOL aircraft to date has been a single engine design with a large, vectored, turbofan engine. The size of the fan, the thrust coming out of the engine (a huge volume but at a relatively low velocity) and the intakes limit the top speed of the harrier family.