Sure, the main limit is this (documented here)
Each account may create only one standing connection to the public endpoints, and connecting to a public stream more than once with the same account credentials will cause the oldest connection to be disconnected.
Clients which make excessive connection attempts (both successful and unsuccessful) run the risk of having their IP automatically banned.
Per the developer policy, you should not attempt to circumvent the connection limit by using multiple API keys / accounts. You are also limited to a certain number of search terms, at up to 1% of the volume of the firehose. There is more information available in the section on making connections.
If you need more than one connection or a larger number of search terms across the whole firehose etc then we would suggest you look at our commercial Gnip offering, which is explicitly designed to handle higher traffic requests.