Given the success of our initiative, we decided to follow it through with further investment.
»He was taken to court because he failed to follow through with a payment plan for the taxes he owed for 1999 through 2004.
to follow through a line of inquiry - расследовать /исследовать/ дело /вопрос/ до конца
1. доводить до конца
to ~ a line of inquiry - расследовать /исследовать/ дело /вопрос/ до конца
2. = follow out