Challenge accepted.
1. Michael I of Russia IOTL has only one surviving son, Alexei. ITTL, his son Ivan does not die in childhood as IOTL and instead survives to adulthood. He also has a third surviving son who wasn't born IOTL named Feodor.
2. The Habsburgs are in the middle of a series of wars with the Ottomans and Russia is one of their allies. The Habsburgs see Tsarevich Ivan as a candidate to restore the Balkans to Christianity and perhaps recapture Constantinople, partly due to his Orthodox faith.
3. To make a long story short, the Habsburgs and their allies are successful and Ivan is named Emperor John IX of the Second Byzantine Empire in 1665.
4. Four years later, Feodor the younger brother of Tsar Alexei I and Byzantine Emperor John IX is elected King of Poland as King Teodor I. He converts to Catholicism upon receiving the crown.
5. This as a result creates three separate lines of the Romanovs: a Russian Orthodox line descending from Alexei I, a Greek Orthodox line descending from Ivan/John and a Roman Catholic line descending from Feodor/Teodor.
6. Emperor John IX dies in 1684 and is succeeded by his son Emperor Michael X. However Michael is a much weaker ruler in the country and regional tensions begin to build.
7. Hungarian nationalism results in independence from the Habsburgs in 1690. Stephen, the second son of Teodor I of Poland (his older brother Teodor is due to succeed his father) is elected King Stephen VI.
8. Following Hungary, Croatia also gains independence from the Habsburgs two years later and selects Michael, the younger brother of Stephen VI as their king, with him adopting the name Michael Tomislav II.
9. The death of Michael X in 1708 sees a balkanization (literally!) of the New Byzantine Empire. The Empire is split three ways between Michael's three sons, his oldest Constantine becomes King of Greece, his second John becomes King of Serbia and his third Nicholas becomes King of Albania.
10. In 1711, Lithuania becomes independent from Poland and Teodor II's second son Peter is picked as it's king.
As a result, Romanovs now have EIGHT thrones: Russia, Poland, Lithuania, Hungary, Croatia, Serbia, Greece and Albania.
Not the most plausible scenario but it's something.
