Is it possible? Yes. Is it easy? No. How do you do it? If I had a magic formula for that, I'd be rich. But...
There is a large body of work "out there" on competitive strategy, differentiation, positioning, market segmentation, etc. I hate to say "go off and read this list of 15 books" but I don't think I can do justice to this topic in a HN comment. So, I will, indeed, just give you a list of books to consider.
Crossing the Chasm - Geoffrey Moore
The Four Steps To The Epiphany - Steve Blank
Positioning: The Battle for Your Mind - Al Ries, Jack Trout and Philip Kotler
The 22 Immutable Laws of Marketing - Al Ries, Jack Trout
The 22 Immutable Laws of Branding - Al Ries, Laura Ries
REPOSITIONING: Marketing in an Era of Competition, Change and Crisis - Jack Trout, Steve Rivkin
Differentiate or Die: Survival in Our Era of Killer Competition - Jack Trout, Steve Rivkin
Blue Ocean Strategy: How to Create Uncontested Market Space and Make Competition Irrelevant - W. Chan Kim, Renee Mauborgne
Understanding Michael Porter - Joan Magretta
Good Strategy Bad Strategy: The Difference and Why It Matters - Richard Rumelt
Hide a Dagger Behind a Smile: Use the 36 Ancient Chinese Strategies to Seize the Competitive Edge - Kaihan Krippendorf
Outthink the Competition - Kaihan Krippendorf
Competitive Strategy - Michael Porter
Competitive Advantage - Michael Porter
On Competition - Michael Porter
Future of Competition: Co-Creating Unique Value With Customers - C. K. Prahalad, Venkat Ramaswamy
Yeah, it's a lot of stuff. I won't say you need to read all of that, but everyone of those books is something that's influenced my thinking, and that I've learned a lot from. If I had to pick one to start with, I'd say the Steve Blank book - The Four Steps to the Epiphany. He does a pretty good job of giving an overview of market segmentation strategies, which you'll probably want to pursue if you're entering a crowded market.
After reading Blank, I'd go for Crossing the Chasm next, then the whole series by Trout, Ries and Rivskin, etc. The Michael Porter stuff is good, but somewhat dry and academic. The Understanding Michael Porter book is a good introduction to his stuff that is a little easier to digest.
Also note a subtle, but important point... there are two different kinds of "positioning* you'll hear people talk about in these kinds of discussions. On the one hand, you have "marketing positioning" as described in the books by Ries, Trout, et al. This is more about the message you send to the market about your firm and your offerings. Then you have Michael Porter "structural positioning" stuff that relates to how your firm "fits" in with your competitors vis-a-vis the "five forces" and the rest of Porterian strategic analysis. One will influence the other, but they are really two different things. Note that anytime somebody starts telling you anything about your "positioning".
And then you have what Bob Parsons (of GoDaddy fame) said "Don't be afraid to enter a crowded market, just be better than everybody else".