A config file can contain many connection strings - all you need is a separate setting for each, or a single setting, and concatenation characters. You can then split the separate settings using the string.Split method.
One way to do it would be to store your strings as:
NameOfConnection:ConnectionString|NameOfConnection:ConnectionString|...
You can then split the string on '|', and break the result into a name / value pair on the first ':'