Yes, according to the Brennan Center, Rod Blagojevich, Governor of Illinois from 2003 to 2009, was technically impeached twice in quick succession.
On January 9th, 2009, the Illinois House voted 114-1 in a lame-duck session of the 95th General Assembly to impeach Blagojevich for various corruption and abuse of power offences - thirteen articles of impeachment in total.
Just five days later, on the 14th, the newly-sworn-in House of the 96th General Assembly voted again to impeach, for the same articles, this time succeeding 117-1.
However, although Blagojevich was impeached twice, there was only one trial in the Illinois Senate. Blagojevich was both convicted and barred from holding a state public office again by unanimous vote.