MetLife Inc. plans to trade its 52% stake in Reinsurance Group of America Inc. for MetLife stock, the companies say.

RGA, St. Louis, will start the transaction by “recapitalizing” its common stock into 2 classes, the companies say.

Holders of the Class A common stock could elect up to 20% of RGA’s directors, and holders of the Class B common stock could elect up to 80% of the directors.

MetLife, New York, would exchange its existing RGA stock for RGA Class B common stock, then trade the RGA Class B common stock for some of MetLife stockholders’ shares of MetLife common stock.

The deal should make RGA’s common stock more liquid, and it will “provide RGA management with greater flexibility in dealing with the opportunities and challenges specific to its businesses,” the companies say.

RGA has a market capitalization, or total stock value, of about $3.2 billion, and that would appear to give the proposed stock swap a value of about $1.6 billion.

The companies hope to complete the deal by Sept. 30.

To complete the deal, the companies need the approval of the holders of a majority of RGA’s common stock owned by entities other than MetLife.

The companies also need regulatory approvals, and they need to see whether MetLife stockholders will trade enough shares for RGA shares to make the deal work, the companies say.

In related news, RGA is seeking of “corporate governance-related changes to its articles of incorporation and ratification of a Section 382 shareholder rights plan,” the companies say.

The proposed changes include a limit on the voting power of directors of a holder of greater than 15% of the outstanding shares of RGA Class B common stock, unless the holder holds an equivalent percentage of outstanding shares of RGA Class A common stock:

Another provision would protect RGA tax assets by restricting other parties from become “5% shareholders.”

RGA’s board formed a special committee consisting of independent directors to evaluate the recapitalization proposal and related transactions.

That committee and the full RGA board have approved the split from MetLife and the shareholder rights proposals, the companies say.

Once the split-off deal is completed, the RGA board probably would convert the dual-class stock structure back into a single-class stock structure, the companies say.