Perhaps *Russia becomes a Cossack Republic? So instead of the imperial Russian system being imposed on the Cossacks, the Cossacks impose their roughly democratic system on Moscow, perhaps copying the Polish-Lithuanian Commonwealth's constitution to formalize their normally informal way of doing things. I don't have a single POD for this, but one idea could be Russia collapses during the Time of Troubles, instead of the Romanovs gaining power. Russia goes from empire to a geographic abstraction, pillaged by both Sweden and the PLC. However, the Cossacks in Ukraine secede from the PLC as per OTL, and retake the territories of Ivan the Terrible as part of an Orthodox Crusade.
While someone is probably elected Tsar, this does not have to be someone too invested in retaining the old status quo (I suggest the nouveau-riche Stroganov family, but I will defer to people who know Russian history better than I). Instead, a (relatively) democratic system is put in place, with a co-equal Tsar and parliament. While citizenship is limited (non-Orthodox are excluded from voting, perhaps requirements for property to vote are put in place as a new elite grows) the resulting system is much more democratic than OTL's Tsarist Russia, and has much greater ability to reform than OTL.