alt Hacker NewsThere were already two exchanges. I don't think this changes much.
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More than that, London and Tokyo both have well known exchanges, and large US companies are often listed on both of those as well. If you tried to tell me that no other country has an exchange I'd call you a lair without bothering to fact check you. (My impression is New York, London, and Tokyo are the big ones that matter in the world and everything else is a me too - but in their niche/country they may still be a big deal)
Most smaller companies are just listing on something like NASDAQ, which isn't confined to a city. With modern computers the idea of an exchange in a city is not nearly as useful as it was 150 years ago.
NYSE, NASDAQ, but also AMEX…
A good overview of the flow of volume through these various venues can be found here. Bottom line - there are more than two exchanges.
There are currently about two dozen national securities exchanges plus a whole lot of alternative trading venues, broker internalisation, and whole market makers that match orders directly. It's a highly fragmented market where one additional exchange will have no substantial impact.