I believe the answer is:
One mutation helps lunch, while your wounds it is healing.
This mutation is: ...ing
giving dressing, a sauce or similar for your lunch, or a bandage for a wound.
In the corporate world one helps you to ceiling.
This mutation is, perhaps, ...for success or ...coat, or power...
giving dress for success or dress coat or power dress, all the same idea of (wearing) attire intended to show that one holds an important position in business.
One is part of a thing that is often sequential
Or is sometimes inspired, often thought presidential.
This mutation is: ad...
giving address; street addresses may be sequential, and speaking addresses, including presidential addresses, are often inspired.
With its friend one can drive you to feelings of shame,
Its friend is, perhaps, ...down -
To dress down someone could well evoke shame.
With friend's brother it gives you a feeling of fame.
Friend's brother is then ...up -
To dress up can make you feel more glamorous or more like someone famous.
One mutation is paramount to sweet acts of couplings,
This mutation is likely: un...
giving undress, an paramount step in paramours' couplings
Then, afterward, It will again hide your dumplings.
The original word, without any mutations, brings us back to dress -
letting you hide whatever sort of dumplings you've got on ya.