There is the possibility for a countless number of dimensions to exist; the world is only stabilized from the viewpoint of the observer. This draws on relativity; a person in a particular dimension is only aware of the dimension he exists relative to. For the Chrono series, the events take place in one dimension (two in Chrono Cross, one being an offshoot of another), called the Keystone Dimension, and later Home and Another Worlds. Dimensions run parallel to one another, never touching save through two exceptions, including multidimensionally aware entities like the planet and Missing Piece situations as evidenced by Serge. Each dimension contains its own history, called a timeline, which can be rewritten by time travelers; the discarded timeline would be sent to a Darkness Beyond Time in this scenario, replaced by a new one with changes by the time traveler.
The only question remaining is, do infinite dimensions exist, or do only a finite amount of realities exist? This question is troublesome for two reasons. Firstly, the Chronopolis researchers speculate that there may be infinite worlds and possibilities; however, the planet of the Keystone dimension exhibits multidimensional awareness. Unless there were finite dimensions that the planet definitely existed in, how could such an entity be aware of other dimensions? Even an infinite number? Secondly, the Time Devourer, main antagonist of Chrono Cross, is stated to be capable of devouring all space-time upon its evolution. However, how can a being of finite proportions devour an infinite number of dimensions?
A clear answer may never be known. Regarding the first problem, it is possible that the planet is simply the same "being" in a few dimensions, but this is a stretch as no information exists on how it was able to pull Dinopolis out of another dimension. The second problem with infinite dimensions may also be resolved if the Darkness Beyond Time only exists for one dimension.