Presumably you are using some form of lubricant for tapping, such as Trefolex, Rocol STD, or as I often do, Bacon Fat? Although not recommended practice, it is possible to go from Taper to Bottoming tap if careful. Many taps break because they are subjected to bending, (You can usually tell if too much torque is being applied, before it breaks). A Tapping Fixture which holds the tap perpendicular to the work avoids bending the Tap.
There is a physical law which says that if you do break it, it will be in the last hole on the final operation of the workpiece.
Believed to be Newton's Fourth Law (of the eternal cussedness of things; sometimes attributed to Sod)
Howard