He worked as spokesperson and strategic adviser of Viktor Vekselberg's Zurich-based investment holding Renova Management AG from 2005 until 2008.

In the negotiations to form a Grand Coalition of Chancellor Angela Merkel's Christian Democrats (CDU together with the Bavarian CSU) and the SPD following the 2013 German elections, he was part of the CDU/CSU delegation in the working group on digital policy, led by Dorothee Bär and Brigitte Zypries.

[4] Blume was a CSU delegate to the Federal Convention for the purpose of electing the President of Germany in 2017.

[5] In the negotiations to form another coalition government under the leadership of Chancellor Angela Merkel following the 2017 federal elections, he was part of the working group on cultural affairs and media, led by Monika Grütters, Dorothee Bär and Michael Roth.

In 2019, Blume co-chaired the CSU’s convention in Munich, alongside Florian Hahn and Thomas Silberhorn.