The Hyperverse contains dimensions from 12 to infinity. This is beyond the omniverse and is higher-dimensional or hyper-dimensional space.
A multidimension can have between 12 and 26 dimensions which is the upper limit for string theory.
A megadimension contains greater than 26 dimensions with countless bridges or subspace conduits between the dimensions.
An omnidimension contains ALL dimensions up to infinity, including infinite-dimensional Hilbert space.
The hyperverse is still within reality but outside the outerverse. Beyond the hyperverse is surreality, the transition between reality and non-reality.