'Open Door' India?

Now, I realize the conditions of the 19th and the 17-18th centuries were different and the idea of an Open Door China was more of an American idea. But could a similar thing happen in India?. OTL, India was completely gobbled up by the British East India Company. Could there be an agreement within the European nations to trade with the Indian with trade posts and spheres of influence, rather than directly controlling them as OTL?
 
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