From a world building perspective, this is how i would describe 2 time dimensions:
1D + time_alpha: A dot moving in {x} space and time{a}. The time line will always be straight.
2D + time_alpha: A dot in {x,y} space and time{a}. The line will now be curved, but only in one dimension.
3D + time_alpha: A dot moving in {x,y,z} space{a}. The line is now free to form in any spacial dimension, but it will always be continuous.
3D + time_alpha + time_beta: a dot moving in {x,y,z} space and {a,b} time.
As {a} and {b} are perpendicular, motion through one is inversely proportional to motion through the other(assuming motion through {a} is constant).
In this case, motion through {a} is no longer guaranteed to be constant, therefore, perceived speed would change depending on one's motion through those temporal dimensions. High velocity through {b} would reduce velocity through {a}, leading to discrepancies in observed and experienced velocity through {x,y,z}.
The result could be large, sudden changes in spatial velocity or position over very little {a}.
e.g. A space ship sets velocity(v) to the 0.5c. 432
It should take 8 years{a} to reach Proxima Centauri. But from the perspective of Earth, it would take 17.4 years.
So, the ship changes it's temporal velocity to move in equal amounts {a,b} equal to the amount that we currently move through {a}. Thusly, motion through {a} is reduced by about 30% (The unit vector ratio of two equidistant perpendicular axes is 0.707).
The journey, from Earth's point of view, now appears to take 12.18 years. From Earth's perspective, The ship has increased in speed, but it has been travelling at 0.5c all this time.
If the ship further increases it's motion through {b}, eventually you could have near lightspeed travel with no appreciable time dilation.
Of course, this is all actually bunkum, but if you are writing a scifi story, it could be just believable enough to the layman to suspend disbelief.
You could add some kind of side effect of moving through {a,b} instead of {a}, like slipping into very close-by alternate realities with only subtle changes. high {b} velocity can take you far from your "home" reality, where the changes are more profound. In such a way there could be some fictional calculus, which describes the rate of change between realities depending on v{b}. 947