Is there any command which is the opposite of
\clearpage, i.e. which goes back a page instead of going forward, similarly to the way you can use
\vspace to move the current vertical position in a page?
No, there is
sampage but that isn't what you want I suspect. The whole memory model of TeX is to ship out pages as fast as you can and to free up the memory. That is why even on the machines of 1982 TeX could produce documents of hundreds of pages. Once a page has been shipped out it has gone.
What you can do is collect more than one page worth of material in a box and then handle the box in some way before shipping it out.