There are limits to how many tournaments a player may have open at a given time.
The number of open tournaments per player will vary by game and tournament type/"flavor".
If you encounter a message indicating you've reached the maximum open tournament limit, you would not be able to enter/begin any additional tournaments of the same tournament type until some of your open tournaments close.
While you may be unable to enter any new tournaments of the same tournament type, you may enter different tournaments available for that game title. You may also re-enter your open tournaments if re-entry is available. (Tournament re-entry is currently limited to specific tournament types.)