If I understand the OP correctly, for example there may be an 8 pg PDF, single pages, ordered from 1-8.
Readers spreads are then required (1+2, 3+4, etc).
Is this correct?
Imposition Studio can easily do this, imposing in readers spreads order and then creating a new PDF.
If this is just for output to print, Acrobat Pro or Acrobat Reader can do this printing via the “multiple” option using the single page PDF.
Sample Imposition Studio layout and linked PDF attached.
Stephen Marsh