Could Joe Lieberman have switched to the Republican Party after 2006?

As many of us know, Senator Joe Lieberman lost the 2006 Connecticut Democratic primary and had to run as an independent, which he ended up winning the general election. Considering how his relations with the Democratic Party were deteriorating by 2006 and beyond, is it possible that he could have switched to being a Republican instead of an independent? If so, how would that have affected the Senate overall?
 
No because Lieberman is not a Republican. Even as an independent he still caucused with the Democrats and had a voting record consistent with the Democrats.
 
As many of us know, Senator Joe Lieberman lost the 2006 Connecticut Democratic primary and had to run as an independent, which he ended up winning the general election. Considering how his relations with the Democratic Party were deteriorating by 2006 and beyond, is it possible that he could have switched to being a Republican instead of an independent? If so, how would that have affected the Senate overall?

Also not possible because the Republicans had already nominated their candidate. He would've been unable to assume the Republican slot on the ballot.
 
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