Yes supply influences how high the price can go, but supply has a slowing effect on price growth. The greater the supply the lower the price, generally.

Comparing Bitcoin and Litecoin is perfect for this talk. Litecoin has 4 times as much supply possibel, 84 millin coins to Bitcoin's 21 million. Therefore, if Litecoin had the same demand as Bitcoin it's price should be 1/4th of Bitcoin's.

The thing that drives price  moreso than supply is demand. If there is no demand for a coin it won't have a high price at all. That's why you're seeing higher prices for coins with greater supply than coins wity the lower supply. The coins with lower supply have much lower demand.

Does this answer your question?