Word for "complementing each other, while showing an increase in intensity"

You are correct that "concurrently" is not the right word. How about "successively"?

"Full Definition of successive 1 : following in order : following each other without interruption 2 : characterized by or produced in succession"

See: http://www.merriam-webster.com/dictionary/successively


Consider subsequently.

Definition: occurring or coming later or after something else.

Example: Mary made a word tour when she was 45. She subsequently devoted her life to writing.