Since the ratification of the Treaty on the Creation of the USSR on December 30, 1922, there has existed several movements to establish new union republics, autonomous areas, and union cities within the Soviet Union. Following the founding four republics, and additional 37 republics have been established within the USSR (not counting the six which gained independence in 1991).
As written into the many constitutions of the Soviet Union, a new union republic may be admitted into the USSR only under the support of the parties involved (via the legislative process). This means that the proposed republic, the Soviet Union as a whole, and any affected republics which are to loose territory in the process.
There has never existed a formal criteria on when a specific area may qualify to become a republic. The general consensus is that a new republic should have a large population (generally around a million) and should have a substantial titular population to assure ethic and regional importance. Prior to the 1990s, there existed a preference for only admitting new republic which were located along the periphery of the USSR to assure any republic the right to secede from the USSR without being enclaved by the USSR.
Arctic Republic and Greater Nenetsia
The autonomous republics of Nenetsia, Taymyria, and Yamalia were established to include most of the land populated by the Nenets people. Since the 1970s and the discovery of natural gas and oil within the regions, the native population has been in decline as Russians and others have begun to develop the region. Beginning in the 1990s, the Nenets began a movement to unite these regions into a single state (on par with the unification of Ossetia). This movement has become somewhat moot since the separation of Siberia from Russia (now dividing the Nenets between two republics).
An alternative proposal has also been made for the same region. Proposed mostly by the settlers and oil companies within the region, the propose uniting all the autonomous republics and islands within the Arctic Ocean and Ob river (i.e., Yugra) and to establish an "Arctic Republic." The combined population of the region is quickly reaching a million people and would be dominated by the gas and oil industry. This alternative proposal has had mixed support and opposition from the native peoples of the region, who would mostly support either a "Greater Nenetsia" or a unified Uralic-speaking republic. The republics of Komi and Yakutia have become the greatest supporters for a new republic within the region.
The historic regions of Galicia and virtually all of western Ukraine have been regarded by those within the USSR as among the most rebellious regions. The citizens of the western Ukrainian oblasts of Ivano-Frankovsk, Lvov, and Ternopol voted against Ukraine remaining in the Soviet Union during the referendum held in March 1991. Much of these regions of the Ukraine weren't historically part of the Russian Empire but were part of the neighboring Austro-Hungarian Empire and later Poland (not becoming part of the USSR until after World War II). It is because of this the region has generally been closer to Europe (especially Poland) in recent years. The region considers itself purely Ukrainian as opposed to the Russified population further east.
While independence is still seen favorably among the residence of western Ukraine (especially following the progress of secessionist movements in Western Europe), many have instead proposed the division of western Ukraine into a new republic.