There are known strategies used by start-ups to take market leadership when they are not the first entrant.
One example is the technology inflexion point strategy. When Symbian OS was the dominant smartphone operating system, it was basically an embedded device operating system made memory efficient. At the technology inflexion point, it was possible to put a 'real' operating system into a phone not an embedded OS. This was the why Mac OS was pruned down and put into the iPhone creating a 'internet in your pocket'. RAM sizes, CPUs, and off-the-shelf GSM modems came in at the time where this could happen.
Product Focus: Another example is to do less than the market leader, but an order of magnitude better. Yahoo was a portal service with search as a popular feature. Google was a non-portal. They take you to your destination ASAP, its the search piece they do but 10x faster.
Another example is price innovation. Bic biros (pens) were incredibly cheap due to mass manufacture, so you didn't need to care after your pen. You just bought a stack. Inferior product but superior price. Disrupted the parker pen and others who wanted to keep charging more for them.
Another example is service innovation. Daewoo cars introduced the Nexus which was a copy car (Astra I think) but they did an inclusive full service over 5 years which was unmatched for volume cars at the time. This made a dent even though they were a later comer.
In answer to your question about how many startups will the VC community support. It depends on the market. Traditionally a mature market will converge to 3 big players. For internet-bedded enterprises its usually the first to scale that is the winner.
If a market carries strategic value, a lesser ran player will still get funding because they will be a strategic acquisition. For example, Apple bought a minor MP3 player company so they could have the basic technology in place so they could get their iPod out in less time to meet a market window.
If we work on 1 in 20 startups succeed, and 3 players dominate in a mature market, there should be funding for 60 players, all else equal. Obviously there are extremes where this does not apply if there is natural scarcity (land) or non-trivial capital requirements at play (eg. chip foundries).
I notice you hadn't been specific in the market you are interested in. So if you would like to go over your practical example, contact me on Linked In, perhaps.