This depends, of course, on what you think of as radical alteration. In many ways, the New Deal did not radically alter American business. However, if you use the term loosely enough, it did.
The New Deal did not fundamentally alter the way that American firms did business. Companies were not nationalized. The government did not step in and try to change to a centrally planned economy. The US continued to be a market economy just as it had been before the New Deal. In that sense, there was no radical alteration.
You could argue, however, that the environment that businesses faced was radically altered. If you feel that the imposition of a minimum wage or a maximum work week was a radical change, then the New Deal did radically alter businesses. The same is true if you believe that the creation of unemployment insurance was a radical alteration.
So, the answer really depends on what sort of change you see as "radical."