In 1921, he won at Buenos Aires (1st ARG-ch) and won a match for the title against Benito Villegas (5 : 2) in 1921/22. He took 7th at Montevideo (Carrasco) 1921/22 (1st Torneo Sudamericano, Roberto Grau won). He tied for 2nd-3rd at Buenos Aires 1922 (2nd ARG-ch, Villegas won). In 1923/24, he won at Buenos Aires (3rd ARG-ch) and won a match for the title against Villegas (5 : 3). In 1924 and 1925, he was declared Argentine champion without official matches (Reca lost a match against Richard Réti 0.5 : 2.5 at Buenos Aires 1924,[2] and won an unofficial match against Julio Lynch 5.5 : 2.5 in 1925).
He tied for 8-13th in 1st unofficial Chess Olympiads at Paris 1924 (Consolation Cup, Karel Hromadka won).[3] He tied for 2nd-3rd at Montevideo 1925 (2nd Torneo Sudamericano, Luis Palau won).[4] In 1926, he lost a match for the title (6th ARG-ch) to Grau (3 : 5). He won at Buenos Aires 1927 (7th ARG-ch) but did not win the title because he refused to play with Grau.[5] He also won at Buenos Aires 1927 (Pentagonal).[6]