Genex Corp., a Rockville-based bioengineering firm, filed plans with the Securities and Exchange Commission yesterday for the sale of 2 million shares of stock for expansion purposes.

This is the second public stock offering in a year for Genex, founded in 1977 to bring the gene-splicing techniques of recombinant DNA from research labsto consumer use. The company, which has 11,560,880 shares of stock outstanding, ran its first public offering last year.

Genex will be selling 1.45 million shares of the current offering. The rest of the stock--550,000 shares--will come from the holdings of Koppers Co. Inc., the Pittsburgh-based building materials, engineering and construction company that is the largest single stockholder of Genex. Koppers supplied venture capital for Genex and now owns 4.32 million shares of the bioengineering firm.

The stock, sold over-the-counter, closed yesterday at 17 5/8, up 1/8.

The company, which has its headquarters in Rockville and its main laboratory in Gaithersburg, plans to use proceeds from the proposed sale for added production and research facilities. Company officials said the question of buying or building facilities depends on which of the present research products is ready to hit the market first.

The company has one product on the market--aspartic acid, a precursor of a new artificial sweetener. Sales of that product are all overseas. Two other products are close to being marketed, officials said.