It was suggested to me to run more races during my marathon preparation. However, races come with both a benefit (more speed) and drawback (risk on injuries). I've been down the more-speed route before, and it turned out to be a dead end, every time.
It's best, for me, to lock in the speed early on, and base all my training on that, including the marathon itself, rather than some elusive shorter time to reach the finish line, if reaching it is already hard in itself.
This is why I think one should race at most two marathons per year, so that one can concentrate in the off-time on getting faster in shorter races. Less is more, also in running marathons as a race (read: trying to get the fastest result). Shorter-distance races during marathon prep should make sense and be part of the preparation, not because you need the thrill of races to pull you through the drudgery of training. If you find your training boring, look for another—more varied and exciting—plan.
Many online marathon plan are safe, and therefore plain, meant for a broad range of runners, and perhaps boring. They are fine for first-time marathon runners, but not so well-suited for those who run their second, third, etc. marathon. They need a more personalized plan, suiting their personality and specific goals. It makes a big difference if your goal is 4.5 hours or 3.5 hours. The first run their tempo runs generally faster than marathon pace, the latter slower (to prevent burnout).
If more races is the only way to keep you interested in running, you might not be a runner. Runners are used to things being predictable and repeatable, most of the times. The excitement comes from improving gradually over time, measured in months, even years. This is why runners keep diaries, a long-time overview of training. Humans are bad at remembering details, especially over a long period of time.
Of course, most people who run marathons do it for the experience, seeing places, be among crowds, which is fine too. In that case, you don't need to limit yourself, and can run as many marathons and ultras as your heart desires and your body can endure. It's your life, your choice how to approach running as a way of life.
Remember though, it's not about quantity, but quality, and variety. So, even in case you run for the experience, less is more. Better to pick the gems than everything that's within reach. You never want an event to become “ordinary.” What's fun in that? You'll lose interest in running after very few of those experiences, however dedicated you might think you are as a runner.
Happy running!