“....In its original form, the Mann Act of 1910 made it a felony to engage in interstate or foreign commerce transport of “any woman or girl for the purpose of prostitution or debauchery, or for any other immoral purpose”. ....”
It was amended by Congress in 1978 and again in 1986 to limit its application to transport for the purpose of prostitution or other illegal sexual acts.
So all that would be required would be to get a definition of “for any other immoral purposes.” Things such as late term abortion could be pretty easily defined as an immoral purpose. What might be a greater stretch would be to “define” the mutilation of either a pregnant woman or unborn child as an “illegal sexual act.”
That could throw a damper on the transportation of women to “abortion friendly” states.
Enforcement of the Mann Act was one of the main reasons the FBI was stood up. Back then called the Bureau of Investigation (BI) and originally it had no arrest only investigative powers. I think it was the Osage Murders that changed that.