This is quite an interesting scenario. Nothing in the regulaions specifies that a person cannot have more than one ASIC. However the relevant people in the department assure me that it the intention is definitely that not more than one card can be held by a person at the same time. The
closest reg that comes to this is:
6.35(4) The issuing body may issue a replacement permanent red ASIC in substitution for a permanent grey ASIC (or vice versa), or an airport-specific ASIC for an Australia-wide ASIC (or vice versa), or an ASIC specific to an airport for one specific to another airport.
I know that still doesn't clearly answer the question though.