Yes, this is possible. However, this is a bit more difficult than performing the opposite procedure, which would be an alar base reduction. A consult with a board certified surgeon would help for you to determine how you may make improvements and create a nose that is in harmony with your facial features. You would need to do a bit of homework, as an experienced specialist would be your best option if you wish to have this procedure. I really hope this helps, and best of luck with your search!
Can Rhinoplasty Widen a Person's Nostrils at the Base of the Nose. Ie: the Alar Base of the Nose?
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Widening of the Alar Base, Nostrils.
I agree with Dr. Naficy. There are aspects of rhinoplasty which can widen the alar base (nostrils). Specifically, if the projection of the tip of the nose is lowered, it may cause the base of the nose to widen slightly. Non-rhinoplasty procedures may also give a widened appearance to the nostrils, such as placing new dental braces or upper jaw surgery which brings out the upper teeth. RB
Although it is hard to tell without seeing your pictures what you are describing is possible with rhinoplasty. See the link below for example.