According to the theory of relativity, there is no specific limit to how much time can be dilated. Both time dilation due to relative velocity and gravitational time dilation can become arbitrarily large under certain conditions.
Regarding time dilation due to relative velocity, as an object's speed approaches the speed of light, time dilation becomes more pronounced. At speeds approaching the speed of light, the time dilation factor approaches infinity, meaning time would effectively stop for the object moving at that speed as observed by a stationary observer.
In the case of gravitational time dilation, the effect becomes stronger as the gravitational field becomes more intense. For example, near the event horizon of a black hole, the gravitational time dilation becomes extremely significant, leading to extreme time dilation effects. However, approaching the singularity of a black hole, where the gravitational field becomes infinitely strong, the theory of general relativity breaks down, and our current understanding of physics cannot predict what happens in that regime.
It's important to note that extreme situations like these are highly theoretical and are not yet directly observable or testable with current technology. However, the principles of relativity allow for the possibility of significant time dilation under certain circumstances, with no inherent upper limit.