Which powers do each of the four ally with?
Austria could join the Russians in settling the Eastern Question, or they could join the Western Allies in defending the Ottoman Empire.
Prussia is probably not yet ready to challenge the Austrians for dominance in Germany, but they may want to deal with the Danes while the British are otherwise engaged; the Russians may also be willing to offer some territorial gains in return for a Prussian alliance, which may, in turn, influence the Austrians.
The Danes may and Swedes may have a reason to support the British and French in the Baltic, but given their potential vulnerabilities to the Russians, they may decide to sit this one out - as they did, historically.
Best,