This is already being done at various levels. Rocket motors, parts, satellites etc are built by various private companies all over the world. Many space agencies provide launch and telemetry services. And, now we've exciting new space-companies like SpaceX, VirginGalactic, Icarus Interstellar etc.

More info:

http://en.wikipedia.org/wiki/Commercial_Spaceflight_Federati...

http://en.wikipedia.org/wiki/Private_spaceflight

http://en.wikipedia.org/wiki/Category:Space_non-governmental...

By the way, ISRO has Antrix:

http://www.antrix.gov.in/