Know-How Exchange : Strategy

In many emerging countries in Asia, a product category is characterized by both a low penetration rate (like ice cream or mouthwash) and a market dominated by a strong leading brand (Wall's or Colgate) with over 60% of market share and many small competitive brands, each of them with less than 5% market share.
If you were a brand manager of one this low profile brand what you would do and what you would not do to increase your market share?

Very curious to get your feedback