What the sense of meaning whole sentence here?
We cannot condone government involvement on what amounts to a privately owned venture.
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We can be involved in a project or venture.
We can also be on a project.
what amounts to means "that which amounts to", that is, "that which comes very close to being" or "that which so closely resembles X that we can rightfully call it X".
Your sentence means, "We cannot approve of the government becoming involved in something which is really a private business venture".
If I say to you that I will not reveal a secret I know about you if you lend me your boat whenever I want to use it and let me use your penthouse suite whenever I am in town, you might say "That amounts to blackmail."