Various studies were done in the past. Recently Boeing launched a stealthier version of the strike Eagle (which is very un stealthy..)
I guess Europe could step in. But the issue is everyone sits on their specific requirements and demands a fair share for their own industry. Hampering every european project. And resulting in e.g. the Typhoon having no stealth, thrust vectoring, range and phased array radar and a substandard air to ground capability. When everyone could see it was a good idea 20 yrs ago, but couldn't change the politically negotiated contract..
Simply giving e.g Dassault the required billions and deadline and have them hire the best euro supply chain is undiscussable.. we demand a fair slice of the pie and country specifics & the costs and planning explodes in our faces..