This sounded like fun so I thought I'd throw in my rough vision. Take what you like and abandon what you don't!
After Russia is forced to pay four trillion Australian dollars to Genetek after the attacks on Moscow and St. Petersburg in 2048, they find themselves in extreme financial hardship. Desperate for money the Russians begin essentially selling positions on the Council of Ministers to corporations with only geneTek being banned from operating within Russia or holding a position on the Council of Ministers.
The executive branch, headed by the President (who is elected by popular vote) continues to run the executive branch of the government and more or less sees to the basic needs of the nation. Military, police forces and the maintenance of all infrastructure not owned by a corporation falls under his purview. He is also in charge of appointing the prime minister who oversees the purchase of positions on the Council of Ministers and acts as an organizer of said ministers.
The country is heavily centralized with most of the population living in the Moscow sprawl, St. Petersburg or another large city. Most of the rural population lives on corporate owned and operated farms, mines, lumber mills, and so on. Corporations own large campuses and arcologies as well as most valuable real estate throughout the country. Public buildings, campuses and the land between them is cared for by the Russian government. As in Withmore, Jurisdiction is a big deal with various companies having extradition treaties with each other and the government but no real authority beyond their borders.
Cloning services are limited to the high and mighty in Russia as there are no GeneTek facilities within the country. This is the one point which the government has truly pushed on all corporations within the country. No GeneTek products or services are permitted at all. Though a few clone data brokers have been able to provide services to the most powerful figures in Russia, it is done with the upmost secrecy and that clone data is transmitted to neighboring countries country. Should such a person die they will "clone out" in a GeneTek facility in a neighboring country ans must discretely make their way back into Russia. Should the death be very public and it can not be passed off as "worse than the reality" an entire new identity must sometimes be taken and strings pulled to grant this new person access to their old wealth. The Bratva has proven very useful in providing smooth transitions (infiltration, new identities and wealth transfers).
Though the Russian government has grown in wealth and power they are spread thin across the vast country and that power is rarely collected in one place for long. Russia also still has a more traditional justice system involving judges, police and trials. Of course, the system is corrupt and the rich will nearly always gain a beneficial verdict.
The Russian government has also taken on a very corporate feel with the President acting as a kind of CEO. Though the president's power has diminished in some ways they are still a powerful and imposing figure to those under their domain. Beyond that, he can, if needed, assemble a fighting force greater than most corporations within Russian borders and has done so on a few occasions (especially when ensuring the anti-GeneTek provisions are enforced).
The average citizen of urban Russia often finds themselves to be visitors of many nations but citizens of none. While at work on corporate property they fall fully under the Corps authority. When they return home to their corporate owned apartment they are now fully under that corps authority. On the transit between they are frequently under the authority of the Russian Government. Though extradition (as mentioned above) is a common and major thing in Russia, there is far less cooperation and information exchange than found in Withmore.
True corporate citizens are those who have been deemed valuable enough to not only hire on but to also provide corporate living arrangements on corporate properties. Such an individuals spend a vast majority of their time on corporate property and rarely step foot onto other corps territories. When they do leave their corp's property is is with corporate transport and under corporate guard and usually just moving from one corporate campus to another.
Rural Russians are frequently born, raised and die in corporate complexes. Working, living and dying for their company. In some ways they are similar to the true corporate citizen but their lives have far less value (nearly none at all) and their pure corporate lifestyle is simple a matter of convenience and expedience.