I have worked with 150 mm² and 185 mm² for supplies to cranes and concrete pumps, as to if you can get over this size don't know.
Common depends on where you work, with construction 150 mm² is common, in domestic it would be unheard of.
Often the larger flex is sold as singles, 16 mm² and above for welding, but with cranes one wants it to auto spool so has to be multi core. For some odd reason auto motive cable tends to be odd sizes 60 mm not 75 mm.
I know I used 16 mm² for a narrow boat, could get 25 mm but hard to get it round tight bends so double 16 mm used.
So 6 mm should be easy, however depends on supplier, and how much they like you, spending £2,000 a month suppliers will go out of their way, one off then hard to find.
The real problem is price, you may find double 4 mm cheaper than 6 mm, this is where it gets interesting. I was talking yesterday to some one wiring a car, to do in Lucas colours would cost arm and leg, so used Bosch numbers instead. We all know 31 is neg and 30 is pos and a box of numbers so much cheaper than all the colours.