[EDIT] In the spirit of asking a "good question", this question is considerably more refined that the one I decided to blurt out earlier thanks to a little additional research and nudges from comments.
I'm not a physicist, but love to let ideas roll around in my head - so please excuse any crossed boundaries. I'm not equipped with the mathematics required to examine or perhaps even pose this question in a way many of you are probably used to.
So, my question:
Spacetime as we know it consists of 3 spatial dimensions + 1 temporal dimension. Is it reasonable to visualise spacetime in our next-highest dimension as consisting of 4 spatial + 2 temporal dimensions?
From another point of view:
If we view our 3D space as a submanifold of a 4D manifold, is it reasonable to suppose that time as we experience it may be a similar submanifold of time in a higher dimension?
Adding and subtracting spatial dimensions is the easy bit (an axis perpendicular to all other axes in that dimension) ... do we also get to add and subtract temporal dimensions from spacetime as we journey from one dimension to the next?
(For posterity, my original question was phrased as "Does the 4th dimension include imaginary time as part of its fabric of spacetime?" - referring to the concept of imaginary time as popularised by Hawking. In case it helps, this annoying little thought experiment arose from musings of the possible mechanics behind quantum entanglement)
References I've found helpful so far:
"Survey of two time physics": http://inspirehep.net/record/532282?ln=en
"Dual field theories in (d-1)+1 emergent spacetimes from A unifying field theory in d+2 spacetime": http://inspirehep.net/record/750980