Yes, this is definitely supported. As Mike Naylor stated, most modern RAID controllers should be able to do this (even desktop systems that support RAID with an integrated controller on the motherboard support this).
The documentation makes no mention of the number of supported disk groups. Limitations are stated in terms of virtual disks, spans, and supported physical disks. As long as your configuration is within those limits, you should be good.
Double Faults and Punctures in RAID Arrays
Based on how much familiarity you seem to have with these controllers and RAID technology in general, I would highly recommend that you read through those two PDFs.
Also note that RAID5 is not generally recommended according to current industry standard best-practices. With the capacities that today's drives are reaching, a 12-disk RAID5 can be particularly prone to issues with data integrity. Don't use RAID5 if the data is important to you - consider RAID6 as an alternative.