You cannot have two ASICs and this very problem has been identified by Issuing Bodies with the Department where a person has an ASIC supplied by their employer but may also need the ASIC for other purposes, ie recreational flying.
Options are: Go to your boss and explain what you are doing. Unless they are a total anal retentive, they should not have a problem with allowing you to use your ASIC. Or, Have your company issued ASIC cancelled and apply for your own. I am not 100% certain but I believe it is possible to process a new application prior to cancelling the previous card. Just so long as the new card is not issued without cancelling the previous one.