The president must call for such new elections after the great coalition fell apart on March 27th, 1930, and after the Reichstag rejected Brüning's budget.
Now, theoretically there could be another chancellor other than Brüning, but would he find a majority for a budget in times of Depression? I don't see anyone else would.
So, 1930 elections it is, even with Marx as president.
And after the 1930 elections, avoiding presidential governments is possible, but it now requires an even broader coalition of even more unlikely allies in even harder times.
Even president Marx might have to appoint Reichskanzler Hitler, if the latter cobbled together a majority in the Reichstag, which is not entirely unthinkable with the results of 1932. But I seriously doubt that Marx would have signed the kind of decrees Hindenburg signed in February 1933 which legalised the dictatorship - and I doubt that Marx would have staged the "Preußenschlag". Without the latter, two thirds of the regional police forces across the Reich would still be loyal to the Republic and not so easily succumb to a Gleichschaltung if the latter had no legal basis whatsoever. So, with a president MArx, Hitler could either have played the long game, using his time in power to bring as many Nazis into positions in the state apparatus as possible before his coalition falls apart, which could help him at a later date. Or he gambles all or nothing, abandons his pseudo-legal strategies and goes full coup, which may or may not have ended up in a civil war in 1933.
Now, if Hitler doesn't manage to get a majority in the Reichstag, I'm not sure Marx would appoint him like Hindenburg did, but it's not entirely excluded. If he did under such circumstances, though, Hitler has less time than above for his machinations because he'll soon face a vote of no confidence in parliament.