Can I program active serial device other than Altera's one using Quartus (programmer) through cable?

Update: I had been wrong in the above, but partially right.

Wrong: the problem was in the ribbon cable. Even native EPCS16 did not work, and I tracked issue down to cable. After cable replacement EPCS16 flashing works, and also W25Q128FV also flashes with EPCS16 setting. I see the following data:

W25Q128FV -- Quartus reports silicon ID as 0x18

Silicon ID (AB): 0x17

Manufacturer ID (9F): 0xEF (Winbond)

Options (9F): 0x40

Capacity ID (9F): 0x18

EPCS16 -- Quartus reports silicon ID as 0x14

Silicon ID (AB): 0x14

Manufacturer ID (9F): 0xC8 (GigaDevice)

Options (9F): 0x40

Capacity ID (9F): 0x15

So we clearly see that for EPCS Quartus reports silicon ID, but for W25Q128FV it reports capacity ID instead. I assume it checks for manufacturer ID, and if it does not know about the identifier, it uses capacity ID as guide for flashing. However there could be an issue with this way of identification: different flash chips may have different sector sizes (64K, 128K etc), and thus programmer will work for chips having same sector size as for selected known chip, but will not work properly if another sector size type is selected (e.g. EPCS128 instead of EPCS16).

Anyway, it seems to be working for my setup.

Now thing I was right in: the business model must change and it is obvious Intel will have to think about simplifying configuration device selection (or even addition of custom) and enhance supported devices list. Moreover Intel does not manufacture these chips, thus it is just a reselling business with questionable (and unsustainable) profits.

And I would like to thank @NYusof for the support, this Intel employee have made a difference.