Yes bungie might have but they brought in other studios to help with the development. And right after d1 release they got into making the second one.
But yes warframe is made and developed by a tiny studio with probly way less funds than bungie and thought the marking might not be as rich as destiny the game / game mechanics and systems are waaay more flushed out.
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Again, wrong facts mate. Stop making things up. They did not bring in other studios to help with the development. Activision are the publishers, they just funded them and bunded them to plans they had to stick on. And no the development didn't start right after the release of D1, it was 1 year later.