Essentially, the TelePort Platinum modem will not work with an ARA Serial Card and RS-232 Cable, as you have discovered. The cable supplies four RS-232 Ports using DB-25 plug connectors. The modem has a captive cable which ends in a DIN-8 plug connector.
A socket DIN-8 "in" cable mounting configuration is rare in the United States. The company that imports this connector into the United States, HB Associates at 510-487-3933, reports that no major United States companies purchase the plug cable connector. They can order one for you from one of the DIN-8 component manufacturers.
However, you will still have to determine the pinouts of the adapter cable, and wire the adaptor yourself, which is not recommended unless you are familiar with this process.
Apple's recommendation is to reconsider using the TelePort Platinum modem with the ARA Serial Card and RS-232 Cable. If you need multiple port access, you should find another modem that either supports DB-25 connectors, or does not use a captive cable with a DIN-8 connector. If you must use the TelePort Platinum modem, you may be able to use the modem port in the Macintosh computer, or try another multiple port card or cable.