Hi Betty,
Ajay is right, you can do upgrade from BO XI 3.1 to BIP 4.1, there is change in the Architecture, BO XI 3.1 is a 32 bit server and BIP 4.X is 64 bit mode.
You have to take this as upgrade project, ordering hardware, installing BIP4.1 SP06(latest), migrating the content from XI 3.1 to 4.1 server..
Ajay have already provided useful links.
Thanks,
Shailu.