Usage of "too" immediately after the subject in negative sentences

I was wondering if the usage of "too" directly after the subject could be used in negative sentences as well, or if it has to be replaced by "either".
For instance:

"I, too, thought he would come."

"I, too, didn’t think he would come." // "I didn’t think he would come either."

Is the first of the last two examples grammatically correct?