[4] From September 2016 until 2018 Socci settled in Mexico in Guadalajara in the Escuela de Boxeo Canelo Alvarez, with the former WBC featherweight world champion Alejandro "La Cobrita" Gonzalez as trainer.

On 21 December 2019 at the event organized by Frank Warren at the Copper Boxe Arena in London, he suffered a technical knockout defeat at 01:55 of the last round against the British boxer Troy Williamson, a bout valid for the vacant IBF European Super Welter title[6] Dario as free agent was the official challenger of Tobia Giuseppe Loriga for the Italian Welterweight Title, which should have been held on March 20, 2020, but which was then postponed to November 13, 2020, in Mantova, due to the SARS-CoV-2 pandemic COVID-19.

The match ended on points with a majority (not unanimous) verdict for the reigning champion, who fought at the home of his managers and promoters Loreni and Ventura, with the three judges assigning the following score: 96–94, 96–94, 95-95.

After a return match in March after an elbow injury, in December 2021 in the province of Salerno disputes the International UBC (Universal Boxing Council) middleweight Title against Georgian, Giorgi Umekashvili (6-0-0), winning by unanimous verdict to the points.

In March 2022 in Berlin in Germany, he again disputes the Intercontinental IBF but this time in the middleweight against the unbeaten Italian-German Vincenzo Gualtieri 18 (7KO) -0-1, who loses on points with a unanimous decision but playing a hard-fought match .