You don't need two ASIC's there is no stipulation in the Act or Regs that requires an ASIC for work and or for pleasure, a company can not stop you using an ASIC which they have supplied, it is your background check and your proof that you have been cleared for unescorted access.
The only stipulation or offence is if you do not have a genuine need to be in a particular place. ie on your day off you hire an aircraft and go flying - that would indicate you have a genuine need to go airside.
On the flip side on your day off if you go to Sydney airport and want to have a look around the tarmac - well then you wouldn't have a genuine need to be there and have committed an offence under the ATSR.
The issuing bodies are responsible for your ASIC not your company. I have one issued be WAC (Perth airport) which is used for work and pleasure. WAC do not stipulate or control how I use it.