A name-brand 199,000 BTU/hr condensing gas tankless would be in order here, and even then it could be a problem with three simultaneous shower flows unless you also installed a drainwater heat recovery heat exchanger.
Rinnai is the worlds largest manufacturer of gas-burning appliances, and have a pretty good support network in the US.
Noritz has a pretty good reputation for quality & support too, and the
NRCP1112 has low pressure drop at high flow compared to older designs.
Navien's
NPE-240A can be a good value at a lower price point than some others, provided local support is good.
The HTP Hydrasmart
RTC-199 is also likely to be a good value, and has lower pressure drop at high flow than most Navien or Rinnai tankless due to newer heat exchanger designs. (It may be identical to the Noritz NRCP1112 under the hood (both manufactured by Kiturami. ) HTP has a bigger presence in the northeast than some players, not sure how good the support is in PA, but they're a decent company that competes on both price & service (in my limited experience, but I can drive to their headquarters & throw a hissy-fit in less than an hour if needed- YMMV
)
If you are heating the place with a natural gas boiler you're almost always better off to use an indirect fired tank operated as a priority zone off the boiler than going tankless, since the flow isn't burner-constrained with an indirect. If you're updating the heating system too there's a much bigger discussion to be had around space heating & hot water, and what makes the most sense.
Three 2 gpm showers going at the same time in the dead of winter with incoming water at 35F and showerhead water at 105F (a 70F rise) the system needs to be able to deliver ~210,000 BTU/hr into the water, which is even more than the source-fuel heat going into a 199,000 BTU/hr tankless. A drainwater heat recovery heat exchanger isn't cheap, but a 4" x 48" or taller unit raises the incoming water temp to about room temperature by extracting heat from the water going down the drain, which makes the "apparent" burner capacity of the units much higher during simultaneous flow draws of a minute or more. In a three bathroom 1-tankless situation it's the showering capacity equivalent of adding another tankless, but at a lower installed cost, and zero operational cost (uses no fuel).
