Can I cover the root of this plant and add plants to the pot?
As far as I know yes you can definitely do that! I would do some research though and make sure you plants that need similar care to the one that's already there.
That looks like a palm tree....I'd repot it and maybe put a couple hanging plants to drape over the edge of the pot.
I would clean out the pot first, make sure all the weeds, etc are out of the pot then replant and add others around it
Those are not roots( as far as I can tell) it's the trunk of the Palm tree,it needs to be above soil level. You can repot higher up & straigthen it out so it begins to grow more vertical upright. You can add additional plants but Palms like good drainage and dryer soil, so plants you are adding will need same bright sunlight, water and soil conditions.
A combination of all of the above would sort your problem and give you a better looking Pot of Plants.
All the above suggestions are great. Another option: I have an over 8' high ti plant in my living room, but the base was pretty bare. I set several smaller pots around base of plant--one of ivy and the other is also a vining plant. They love it there and have grown to overflowing. With just adding other potted plants, you can try different variations if one doesn't work out.
Thank you all so very much. This plant is at a house I am renting. I just hate to see plants die because of neglect.