By Bruce Levine–

(CBS) The White Sox are once again going for it in 2016. Any thought that management was considering tearing down the infrastructure of the 25-man roster was eliminated after the recent trades for and signings of veteran players.

So, would a Cuban connection work for the Havana-friendly Chicago franchise by adding another power hitter?

The additions of Todd Frazier, Alex Avila, Dioner Navarro and Brett Lawrie suggest another two-year window approach is coming for the White Sox. Frazier and Lawrie are under team contract control for two more seasons. Avila and Navarro have one-year deals.

The White Sox scored the third-fewest runs during the 2015 season. That means 13 of 15 National League teams outscored the Sox without the DH slot available. Repairing those obvious run-production needs has been the top priority of general manager Rick Hahn. The team needs one more RBI man. This slugger is needed before the White Sox turn their complete attention to finding another starting right-handed pitcher.

Ideally, a left-handed bat like free agent outfielder Alex Gordon would be perfect for the White Sox. Gordon averages 19 home runs and 75 RBI per on 162-game slash lines. Along with his Gold Glove defense, he will be a solid addition anywhere he lands in a lineup, with a career .348 OPS.

In the case of the Sox, a more robust slugging type may be desired. At 28, Justin Upton has a .271/26/84 average per 162 games. Those numbers are closer to what the club needs going forward.

Maybe the Cuban route and Yoenis Cespedes would be the ideal direction to drop your $100 million line into the free-agent waters. Cespedes played left field in leading the New York Mets into the World Series, and he may be the right choice. He has big numbers, and the culture that would seem to fit between him and the White Sox.

The numbers and his heritage say instant connection. However, the case-by-case study may be more telling than just painting with a broad brush. Saying every Cuban hitter will fit with the White Sox because of their history with Cuban stars wouldn’t be doing the due diligence necessary. Cespedes has the numbers and the experience to at least kick the tires on a signing.

“This guy is a better player than Gordon,” said an American League coach who watched Cespedes first-hand. “Cespedes played great for us, and he is an outstanding left fielder. Gordon is a fine player, but overall, (Cespedes) has more impact every day. He can be pitched to, but he hits mistakes as well as any player in baseball.”

The White Sox’s payroll is right at $110 million going into next season. The team has earnestly tried to move Adam LaRoche and his $13 million figure for 2016 with little success so far this offseason. Not one player of this free-agent outfield group will want to settle for less than a $20 million annually on the long-term deals they agree to. Jason Heyward’s $184-million deal over eight years with the Cubs is the template for these top run producers left on the street right now.

In the case of Cespedes, he wouldn’t have to be the Sox team leader, and he would have fellow Cuban Jose Abreu as support, in what would be an imposing lineup if Chicago is his destination. He will average 30 home runs and drive in 100 in a 162-game sample size. He’s not afraid to mash with the game on the line; Cespedes hit .312 with nine homers and 68 RBIs with runners in scoring position in 2015.

Will the White Sox take their payroll up to $130 million in 2016? That’s a question that will be answered soon, as we see the potential landing place for Cespedes, Gordon and Upton over the next few weeks.

A lineup with three potential 30-home run and 100-RBI sluggers would be fun to project and watch develop if Cespedes joins Abreu and Frazier in Chicago.

Bruce Levine covers the Cubs and White Sox for 670 The Score and CBSChicago.com. Follow him on Twitter @MLBBruceLevine.