Theoretically, there is no maximum provided pixels can get infinitely smaller or a screen can get infinitely larger.
Practically, there is a limit to how small a pixel can go, so a 32 inch screen for instance would have a maximum pixel density of let's say 50k (not accurate at all). You can make the screen larger to fit more pixels in, but would 1) reach a maximum realistic size limit for a screen or 2) reach the point where a screen no longer fits within your line of sight.