[adrian_b]

Yes, but you transition between the 2 modes with far jumps, far calls or far returns, which reload the code segment.

Without passing through a far jump/call/return, you cannot alternate between instructions that are valid only in 32-bit mode and instructions that are valid only in 64-bit mode.

Normally you would have 32-bit functions embedded in a 64-bit main program, or vice-versa. Unlike normal functions, which are invoked with near calls and end in near returns, such functions would be invoked with far calls and they would end in far returns.

However, there is no need to write now such hybrid programs. The 32-bit compatibility mode exists mainly for running complete legacy programs, which have been compiled for 32-bit CPUs.