Spreading the trading thin on multiple exchanges is not good for a small volume coin.
As bible_pay said, it's probably the other way around - new exchanges should actually increase volume and price, and not distribute volume out and lower average value. At least that's what I've seen in experience with a couple of coins. It's because those new exchanges hold thousands of buyers who are using only that exchange.
For example, take a look at this recent quote from this very thread:
Currently I cannot buy because I only trade at Cryptopia.
Also, every exchange has some way to discover new coins, so a lot of people first hear about a coin when they see it on their exchange.