I just checked that PC's spec on ASUS' website, and it says the highest wattage PSU they use in that PC is 350W.
https://www.asus.com/us/Desktops/M11BB/specifications/
Something like a R9 270X is only gonna run on a decent 500W supply (with 28A on the 12V rail), so I'd definitely recommend upgrading the PSU first, before making any changes to your system.
😀
P.S: The actual CPU part of the A8 APU performs similarly to the Athlon 860K. @jerdle No offence, but you must be stupid to use anything over an R9 280X or GTX 960 with that A8.