You can pick up optional jobs along the way - collecting for loan sharks, for example, or running a quick street race - but none of these are particularly fun or interesting. So you'll often find yourself taking long, uneventful drives just trying to advance the story - unless you run into a cop.
Police in Parallel Lines are very touchy, and will come after you if you so much as speed or run a red light near them. Worse, no matter what your crime is, the cops’ response is always to try to run you off the road and kill you. This means that your "felony level" (which nudges up with every crime you commit) will skyrocket quickly. You'll frequently find yourself fleeing the police with a full felony level, wondering what just happened and looking for a safehouse to hide in.