This expression is often used to argue
against an "add and stir" approach. This would be, for example, hiring a few women without changing any family leave policies or creating any workplace flexibility. So the stir here means incorporate into the existing structure, without changing it. I'm working on an article where I'm trying to think through whether or not the Colombian peace accords just added LGBT and stirred, or how much adding LGBT to the accords really changed the overall approach.
I saw this translation used by Serrano Amaya in
Serrano
Amaya, José Fernando. 2013. “Agenciamiento E (in) Visibilidad de La Diversidad
Sexual Y de Género En La Construcción de Paz.” In Paz Paso a Paso: Una
Mirada Desde Los Estudios de Paz a Los Conflictos Colombianos, edited by
José Fernando Serrano Amaya and Adam Baird, 53–78. CINEP y Editorial Javeriana. available here