Great question. I don't think one can argue that business was radically altered by the New Deal nearly as much as it was altered by the Great Depression itself. Massive numbers of businesses failed as the economy contracted at that time, and large public works programs such as the Civilian Conservation Corps, Public Works Administration and Tennessee Valley Authority, if anything, helped some businesses to survive through the leanest of times.
Perhaps the biggest long term influence of the New Deal on business was the legalization of collective bargaining rights in 1935 under the National Labor Relations Act. This finally legitimized unions and gave workers the right to join them. These unions then negotiated contracts that gave workers advances for the middle class in terms of pay and benefits, but dug into the bottom line of companies.
There was an attempt by FDR to more strictly control business prices and production with the National Recovery Act, but this program was struck down by the Supreme Court in Schechter v. United States. So its impact on American business was blocked by the judicial branch before it had a serious effect.
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."