Great idea. I don't think it will work. From what I can tell, you can't have 4.
The OMAP5 has one SD/eMMC interface and two SDIO interfaces.
http://images.anandtech.com/doci/4153/omap5.png
This picture is not supposed to be an exhaustive feature list. It's just an example configuration for promotional purposes. Read section 24 in the TRM:
http://www.ti.com/lit/ug/swpu249y/swpu249y.pdf
There are five SD-capable ports (MMC1 through MMC5), with one of them being capable of eMMC and the other three capable of external SDIO. However, only of these ports supports 3V, meaning that the others may need some kind of level shifter/transceiver to interface with SD cards. From what I can find SDHC and SDXC cards can run at 1.8V natively so this may not strictly be the case.
Also, apparently only MMC1 has CD (card detect) and WP (write protect) pins so this could be a headache for one of the externally accessible SD slots, maybe they'll have to be wired to a GPIO and monitored in software instead..