Each implant can hold a single key at once (or in the case dual-frequently implants like the NExT and xMagic, one per frequency) but they can be reprogrammed on the fly within limits.
For your use case, I’d find out more about your work badge first. Learning more details about the existing set up will help you determine what to get and what tools you can manage it with. If it is a low frequency card then you will probably be able to clone it easily. If it’s a high frequency card, you might be able to clone it if it’s the type that a Magic chip can work with. Alternatively, if you are friends with whoever manages the system then you might be able to enroll an implant without having to clone an existing one.
For your house, if someone other than you (property manager, etc) has control of the security, then you will need to repeat the same steps and learn more. If you’re putting together your own system, then you can enroll whatever you want in it. You may even be able to use the same credential more than once.
As for how to learn more, brands or models on your cards or the readers might help. If you have a NFC-enabled phone and you’re able to get a scan with Taginfo, then you know it’s a high frequency card and plenty of helpful details. If not, then it’s either a low-frequency card or a high-frequency card that your phone doesn’t know how to read. You can also use a RDC card or a Proxgrind RFID detector to sense if your reader is emitting a low frequency or high frequency field. (Or both.) If you have a PM3 or a Flipper Zero, you will be able to scan your card and learn what you need to know.