Handgun ammo can't have a solid tungsten core or it will fit the federal definition of armor piercing.
However, as I read the law, a powdered tungsten core mixed with a significant amount of other ingredients might be legal.
Tungsten is about 70% more dense than lead which means that a 109gr lead bullet would be about 185gr if it were made out of tungsten instead. In other words, it shouldn't be that difficult to take a typical 9mm bullet and make it into a super-heavyweight bullet using some kind of frangible core made up primarily of tungsten powder. That gets away from the problems with an excessively long bullet taking up all the powder space.
But there's still the issue of propelling that extra mass to usable velocity without excessive pressure.
As far as recoil goes, 185gr at about 950fps shouldn't recoil prohibitively--that's an unremarkable .40S&W loading and we know that 9mm and .40S&W guns can share a virtually identical form factor and weight.
So maybe not really that difficult of a problem to solve... But still interesting.
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