Today I experimented and came up with a excellent tasting white whole
wheat - Irish Oatmeal Sourdough bread. The ingredients a

2 cups of Carl's starter cultured in red whole wheat flour
1-1/2 cup water
1/8 cup vital gluten
¼ cup milk powder
1 tsp salt
1 cup cooked McCann's Steel cut oats (I doubt if rolled oats would
work)
5+ cups white whole wheat flour (King Arthur's)

I brought it together in my Kitchen Aid mixer with a dough hook using
only 4-1/2 cups of flour. After it came together, I added ½ cup and
maybe more flour until the dough came to correct state for kneading
with the dough hook. I then let the mix knead for about 10 minutes. I
covered the bowl and let the dough rest for 30 minutes. After the
dough rested, I turned the dough out onto my floured kneading board
and kneaded it for about a minute, Then I split the dough into 3 and
kneaded each piece for about 6 to 10 minutes. Each piece was then put
into a warmed clean bowl covered and left to rise for about 2 hours.
After the rise, I shaped each piece into a loaf, put them on a piece
of parchment paper on a sheet pan and covered them with a damp tea
towel. I then preheated the oven to 350 degrees, (the racks are
layered with quarry tiles.) When the oven got up to temp, about 20
minutes, I slashed the loaves and slid onto the tiles. I also put in
a pan of boiling water into the oven. They baked for 55 minutes.

The loaves are very flavorful but a little dense. But what would
expect mixing whole wheat and steel cut oats.

BTW. A tip from a person who eats steel cut oats daily, a very easy
way of making cooked steel cut oats is as follows. The night before,
bring 4 cuts of water up to boil in a pot. Add a cup of steel cut
oats and stir until it comes up to a boil. Take the pot off the heat
and cover pot. Leave it on the stove top until the next morning and
you now 4 cups of cooked oats perfect for microwaving for breakfast or
adding to a bread dough. It keeps well in the fridge. (When you open
the pot, you might see a green color - it is not mold - it comes from
the oats.)