He made his 100th and final Chacarita appearance in May 2018, featuring in a Copa Argentina match with Deportivo Maipú.[1] On 15 June, Rodríguez completed a transfer to Nemzeti Bajnokság I side Ferencváros of Hungary.[5] Six appearances followed in all competitions in five months, with the midfielder leaving in January 2019 to join Universidad Católica of the Ecuadorian Serie A.[6][7] His first appearance came in a win away to Técnico Universitario on 11 February, while his last would arrive on 2 November against América de Quito.[1] January 2020 saw Rodríguez switch Ecuador for Colombia by joining Cúcuta Deportivo.[1]
Rodríguez scored goals versus Deportivo Cali and Independiente Medellín across fifteen appearances for Cúcuta Deportivo in 2020, a campaign that ended prematurely for the club after they were liquidated.[1] Earlier in the season, in February, the midfielder was fined $52,668,180 and suspended for two matches after being charged of deceiving the match officials to win a penalty against Alianza Petrolera on 8 February; the country's player union called the fine "disproportionate".[8] He was the first player to be punished for that offence under new legislation.[9] Cúcuta had previously been unable to pay wages to their squad.[8]
In February 2021, Rodríguez returned to Argentina and joined Alvarado.[10]