This are very rough ideas.
Imagine requesting a page, identifying the start and end of the parts you are interested in, setting the BASE tag as appropriate, and leaving the contents of the HEAD section. That may deliver a functional page segment.
The idea is to pull in content from a page, that may not be constructed to deliver its content in segments. In other words, a traditional web page, intended to function as a unit - not a collection of elements.
Later refinements could filter unused elements to reduce the bandwidth requirements.