What was the most number of independent states that simultaneously existed within the Holy Roman Empire?

There are no real estimates of just exacly how many independent political bodies existed at any point within the Holy Roman Empire, partly because the definitions and degree of sovereignty of individual statelets was often vague and partly because ownership of territorial enclaves was often a contentious and controversial matter. I'll be following this answer myself in case someone better acquainted with the topic than me is able to provide a more accurate estimate.

At the end of the 17th Century, the Kleinstaaterei was arguably at its greatest, with over 1800 individually demarcated territorial stretches divided amongst around 300 to 350 more-or-less sovereign political bodies.