Yes you can, though I don't think true "enhanced IDE" drives are still manufactured, they have since be long replaced with more current ATA specs.
EIDE did not add supported for larger than 504MB drives. Enhanced BIOS did which is not related to EIDE. Confusing to say the least. EIDE added support for ATAPI devices (non hard drives), dual channel support and most of the features including increased transfer rates that were eventually introduced in ATA-2. Also the original ATA spec had both single and multiword DMA modes in it, so EIDE didn't add DMA support either, it just introduced faster versions.