Well, once you get your PPL and IR, you just move on to the
multi-engine by renting a Piper Seneca and working your way up to the
LJ, or go directly to the LJ. I hear they are not all that hard to
fly. I have no idea what the rental cost would be, but fuel alone for
those babies costs a mint. You'll probably have to rent from a flight
school, and they charge more than your local FBO who might have a twin
available for training.

As others have said, just a matter of time and money. I might also add
aptitude, since some people turn out to have no ability to fly.