As others have suggested, depending on what you want ultimately to do wheel cutting wise, a time and strike clock can be built with 3 cutters. Of course, that calls for a bit of careful planning. But, one cutter for the wheels, one cutter for the pinions, and one for the escape wheel will suffice. The same cutters can deliver the strike side components also.
Where this falls into the abyss a bit is the need for 6-7-& 8 leaf pinions in many clock configurations/trains. 7&8 leaves are pretty traditional in many trains. It is customary for using a 6 leaf pinion for the motion works idler paired with a 72 tooth hour wheel. So, what to do to do it with only the 3 cutters? Obviously, any clock we might hope to build will have certain limitations as to how large a wheel can be, how much fall do you have for a weight, or how long /width spring is to be used, how long of run time is desired, and so forth. If we are to select say an 8 leaf pinion that choice will certainly limit a bit the tooth counts we will have on our wheels. 6 leaf pinions in the drive train is not a recommended choice, they are quite in-efficient in that sort of work. Using an 8 leaf idler pinion will require a higher tooth count on the hour wheel and since we only have one wheel cutter in one module the dia of that wheel may get to be a bit large, to yield a 12:1 ratio. We can work around all those things, but compromises are required. It is easier on all if we can cut 6,7,& 8 leaf pinions for our work. 5 cutters will give you a ticking clock better than limiting yourself to just 3. But at $150 each for Thorntons' best, it can be painful.
When it comes to cutting wheels and pinions for repair work, or for the trade, one of everything is best. And everything is a moving target you will never completely accomplish. Jerry K's approach of making one's cutters for a specific wheel or pinion would be preferred over mine of buying many commercial cutters. By today's prices I most likely have over $30k in commercial cutters, and I have needed to make several cutters for special clocks in the last year. (escape wheel for a tower clock, 3 different sized cutters for Ives Brooklyn model clock movements, a great wheel for a woodworks, on and on) So, the making of and successful use of fly cutters per Jerry's (and others') approach makes a lot of sense to me.