I do not currently have any way of trying this without LM317 regulators, and cannot seem to find an answer anywhere.

Its a question of whether or not connecting together a set of regulators like LM317 in a series type configuration will have an effect of increasing the maximum voltage limit able to be regulated. Will such a configuration result in this happening?

 

Hello,

What will be the input voltage?
What will be the output voltage?
To reduce the voltage on a regulator, you can use a second regulator that will drop the preregulation:



This is taken from an old national datasheet.

Bertus

 

This is taken from an old national datasheet.

The problem with that connection is that the full input voltage likely will appear across just one of the regulators if the output is shorted.