Is this a question about Python (a) or having multiple IPs on the server (b)?
If (a) then yes, you just have to bind the socket to a particular IP address that you want to use. For example:
s = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
s.bind(YOUR_IP_ADDRESS)
s.connect((REMOTE_HOST, REMOTE_PORT))
Anticipating a question about the urlopen, pls look at my comment on StackOverflow
If (b) then you just configure additional IPs in the /etc/sysconfig/network-scripts/ifcfg-eth0:X
/where X is a virtual interface ID, 0, 1, 2, etc) (assuming that all IPs are on that interface. If they are not then provision them in ifcfg-eth1, etc)
Once the configuration is in place, restart your network: service network restart