Is it possible for shareholders in private limited companies to sell their shares to anyone willing to pay for them, if the shares have already been offered to existing shareholders who have declied to buy them ?

The reason I am asking is I am looking into the possibility of setting up a web site where people interested in buying and selling shares in private limited companies would be able to come together to make the trades. Would it be legal to set up such a web site ? or are there reasons why this could not be done ?

Thank you very much for your help


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