Much of the bitterness in breads made from whole wheat is caused by the phenolic acid and tannins in the bran layer of the wheat. Different varieties of wheat have different levels of those compounds and produce breads with different levels of bitterness. "Traditional" varieties of wheat, such as red wheat, contain high levels of tannins, while hard white spring wheat contains relatively low levels of tannins.
Here is what bakingbusiness.com has to say about this subject:
With whole wheat, taste differences boil down to the tannin content of
the bran. These red pigments in hard red wheat carry a bitter flavor.
“... Whiter whole-grain varieties typically contain fewer tannins, which
results in a less bitter taste,” said Brook Carson, technical product
manager, ADM Milling, Shawnee Mission, Kansas. "Differences in taste can
also be overcome with added sweetness or with a masking agent."
Based on your question, it sounds likely the Pillsbury Chakki Fresh Atta whole wheat flour you use for making parathas is milled from either hard white spring wheat or a blend of the white wheat with a more traditional variety of wheat resulting in a non-bitter end product.
There is another possible source of bitterness in bread made from whole wheat flour, although it shouldn’t really affect commercially made bread. When whole wheat flour is milled, it includes the oil containing wheat germ, which is different than refined white flour where the wheat germ is removed prior to milling. This oil in the whole wheat flour results in it having a much shorter shelf life than white flour and makes it susceptible to rancidity if not stored properly. Commercial bakeries go through (literally) tons of flour, so their whole wheat flour shouldn't be sitting around long enough to go bad.
I can tell you from first-hand experience, one of the signs whole wheat flour has started to go rancid is an increase in bitterness.
Part of the problem is that whole wheat flour goes rancid pretty quickly after it's milled (I believe it's from the natural oils in the germ). The usual advice is that whole wheat flour has a shelf life of six months or so, much less than white flour. If you're using old flour, try getting fresher stuff.
If you're willing to go through extra effort, consider milling your own whole wheat flour; after reading this article: http://www.realbakingwithrose.com/2006/11/rose_levy_beranbaums_100_whole.html I got a grain mill attachment for my KitchenAid mixer and started milling flour, and I've become a total convert. Fresh-milled whole wheat flour has an incredible taste. My standard loaf these days is 50% whole wheat and 50% bread flour, and it tastes great. It has a nice nutty flavor without the tree bark or cardboard you'd normally associate with bread with so much virtue in it. I've done 100% whole wheat loaves before, and while they're very good, they're just not my thing.
If you want to get even further into it, Peter Reinhart has a book on whole-wheat bread making, which has special starter techniques to get the best flavor possible. I realize your question is about biscuits and not necessarily bread, and his book doesn't have anything to say about biscuits or quick breads.
Best Answer
I mix all kinds of things into my bread, so yes, you can do it.
Things to note: if you add things that draw water, you may want to either soak them first (i.e. seeds) or add more water to your dough (i.e. oat flakes, which would loose their structure when soaked).
I don't know how you raise your bread, but in case let the dough raise, then knead again for a second rise:
You may want to put in your additions after the second knead (to make sure your yeast stays undisturbed for the first).