I too can be rewritten as I also. It denotes an agreement with a previously stated position or action.
"I too "expresses support for something that what the speaker has referred to earlier.
"I too" expresses an identification. The identification could be with a position, a group of people or actions.
J. F. K. used this technique when he stated that he too was a Berliner in support of the people of Berlin after the Berlin airlift.
( that he said it in German added to the sense of identification.)