Depends how you define planes. I guess you could say that there are an infinite number of planes to represent the infinite possibilities in space and time. If you think of time as a path with many possible turnings you could take any turning but the other branches of the path will still carry on even though you are not on them. They exist in a parallel universe. I believe this.
Can we assume that planes are extrapolations of dimensions? For example our plane resides in the first 5 dimensions? They say we can move freely in the 3 dimensions of space, we move in a straight line in the 4th dimension of time and we stand still on a spot in the 5th dimension. But what is beyond that? If you believe in the infinite universes of the infinite possibilities of time, we can say that there are parrallel universes that exist in the same physical space yet we do not perceive them as they are on an alternative time plane. If you catch my drift.
Scientifically speaking, I have heard scientists speaking about 15th dimensions etc. For example the super-string theory about everything, even space being made up of super strings that reside in the (I can't remember) something like 8th and 9th dimensions. They can apparently detect them in a way that a 2D world might detect the 3rd dimension. In a 2D world if a 3D man steps on it, the 2D world will detect his shadow as well as the infinitely thin sole of his foot. In the same way apparently, scientists have detected the shadow of these super-strings from teh higher dimensions. I'm a bit skeptical...you should read up on the super-string theory as it's probably the closest you'll get to scientific "evidence" for higher dimensions and other planes existing.
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Too set in his ways to ever relate
If he could set that aside, there'd be heaven to pay
But weathered and aged, time swept him to grave
Love conquers all? Damn, I'd say that area's gray
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