In short, yes.
A difference-in-differences (DiD) model can accommodate multiple discrete treatment variables, even continuous treatments. If your data is granular enough, it is appropriate to replace a discrete treatment variable with a continuous one, assuming you know the concentration of late-night livery vehicles in circulation within your cities. Alternatively, you may also want to partition cities into either a high- or low-intensity subgroup. This is useful if your cities clearly fall above or below some pre-determined intensity threshold. If you proceed with the latter approach, I also recommend collecting data on cities never espousing the late-night taxi policy, though this may be difficult in practice. If you do obtain a suitable group of non-adopter cities, then this would serve as your reference group. However, if no such cities exist, then it is also permissible to force the collection of low intensity cities to be your reference group. By dichotomizing treatment in this way (i.e., high versus low), it is the same as the traditional binary DiD approach. The only difference is now you're investigating the 'added effect' of shifting from a 'low-dose' city to a 'high-dose' city.
I should also note that treatments may also vary greatly across cities in terms of the "type" of services (and vehicles) available. Data permitting, it is also possible to include separate discrete treatment variables for the different treatments. A concern, however, is when multiple livery services (and car types) operate within the same city jurisdiction. How will you 'tease out' the effect of your late-night car service policy on drunk driving arrests if the city is flooded with a mixture of vehicle types (e.g., sedans, vans, sport utility vehicles, etc.), each with an allegiance to a different commercial agency? If you're in control of treatment assignment, then you may allocate different cities receive different transport services, or widely different vehicle types. But this is wishful thinking. If you're not in control of this process, then it will be difficult to isolate the different exposures across jurisdictions. In some cities only one particular type of car service may be permitted to pick-up passengers; this is something you could exploit. Despite their ubiquity in the global market, Uber and Lyft do not operate within a small subset of jurisdictions around the world. It might be worthwhile to gather arrest data in jurisdictions where you know legislation explicitly excludes a particular types of car service—or car type.
I also encourage you to investigate differences in arrest laws/policies across city jurisdictions. I don't know how big your study is, or is going to be, but if you're acquiring data on cities globally, then this is something you must consider. The police in some Scandinavian jurisdictions define the term "vehicle" a little more broadly than other locales. For example, try reading about the Norwegian man arrested for impaired driving while operating a Segway (And no, I’m not kidding). And what about differences in how punishment is meted out in vastly different regions of the world. In the United Arab Emirates a person convicted of drunk driving may be whipped (And no, I'm not kidding). Do you think this might influence the consumption of alcohol in the adult population? The foregoing examples may seem a bit extreme, but they should be considered. Even if you restricted your sample to cities within the State of Texas (U.S. jurisdiction), for example, then you would still discover differences in reporting practices across law enforcement agencies, not to mention some of the large metropolitan police departments have the resources to dedicate entire units to drunk driving enforcement.
Lastly, is the introduction of a late-night taxi service truly exogenous? Would city officials push for more legislation, in part, due to a recent surge in traffic fatalities or drunk driving arrests? I encourage you to think hard about such questions if you're proceeding with a DiD approach. And, in my experience working in city government, I would presume different cities will institute their policies at widely different times, even in response to the demands of senior officials at the highest levels of the governance hierarchy. If so, then I encourage you to use the 'generalized' DiD estimator. Peruse the following article for a gentle introduction to the method.
