If you want to play BlazBlue: Continuum Shift Extend (or any BlazBlue for that matter!) on PlayStation Vita you have to buy the game on a Vita cart. Arc System Works already released BlazBlue: Continuum Shift for PlayStation 3 and Xbox 360. So, will you be able to upgrade?
The answer from BlazBlue series producer Toshimichi Mori is no. You won’t be able to purchase downloadable content to turn Continuum Shift into Continuum Shift Extend.
Mori also explained to Siliconera each version has its own online modes and are not compatible with each other. Similar to Super Street Fighter IV, you won’t be able to fight someone who owns BlazBlue: Continuum Shift if you own BlazBlue: Continuum Shift Extend.
BlazBlue: Continuum Shift Extend will come out for PlayStation Vita, PlayStation 3, and Xbox 360 on December 17. Development originally started for Vita, but Mori felt like fans on consoles shouldn’t miss out on the new scenarios and began development on a console version too.