You cannot simply change one thing in your drivetrain to more gears and assume it'll be fine.
The cassette and shifter can be changed and it will kind of work ...
BUT:
-your chain will be too wide for your cassette and so you'll need a new 9 speed chain.
-your front chainwheels will be too wide for your new chain and so they will possibly start damaging it.
-your front derailleur will have a cage that isn't suited for your specific chain anymore and so it might not shift smoothly anymore.
-your rear derailleur will also not be made for your new chain and possibly have issues.
Bottom line: a drivetrain should consist of parts specifically designed for a certain amount of gears on the cassette ... you shouldn't interchange between the various systems.