How can I reliably find out, if a Computer supports SATA Port Multiplier or not?
Is it booting a live linux and issuing dmesg?
Consult the manufacturer of the motherboard, or the manufacturer of the SATA Controller if there's a separate controller in a card slot which controls the drive(s) now. You can run dmidecode from a Linux LiveUSB to determine the make and model of the motherboard, when you look on the Devices | DMI page.
However, just adding a new SATA Controller will probably yield faster drive service, as Port Multipliers share the available bandwidth from the SATA controller they are attached to.