Mya variabilis Maton, 1811
Maton, 1811. Trans. Linn. Soc. London 10: 327, pl. 24, figs. 4-7.
(renamed Hyria matoni Gray, 1825)

Diplodon (Cyclomya sec. Bulloideus) variabilis — Simpson (1900), Simpson (1914)
Unio variabilis — Corsi (1900)
Diplodon (Bulloideus) variabilis — Haas (1931), Thiele (1934), Haas (1969)
Diplodon variabilis — Bonetto (1959), Schade (1965), Parodiz (1968), Graf & Cummings (2021)
Diplodon (Rhipidodonta) variabilis — Parodiz & Bonetto (1963), Bonetto (1965), Figueiras (1965), Pereira et al. (2014), Torres et al. (2018)
Rhipidodonta variabilis — Simone (2006), Graf & Cummings (2007), Bogan (2010), Mansur et al. (2020), Torres et al. (2024)
Diplodon (Rhipidiodonta) [sic] variabilis — Rumi et al. (2008)

Mytilus membranacea Maton, 1811
Maton, 1811. Trans. Linn. Soc. London 10: 329, pl. 24, figs. 11-12.

Glabaris (s.s.) membranaceus — Simpson (1900)
Anodonta latomarginata — Corsi (1900)
Anodontites (s.s.) membranaceus — Simpson (1914)
Rhipidodonta variabilis — Simone (2006)

Hyria matoni Gray, 1825
Gray, 1825. Ann. Phil. 9: 138.
(new name for Mya variabilis Maton, 1811)

Unio matoniana d’Orbigny, 1835
d’Orbigny, 1835. Mag. Zool. 5(61-62): 35.
Type(s): BMNH_1854-9-4-50, Rio de la Plata, Buenos Aires, Argentina.

Diplodon (Cyclomya sec. Bulloideus) variabilis — Simpson (1900), Simpson (1914)
Unio variabilis — Corsi (1900)
Diplodon (Bulloideus) variabilis — Haas (1931), Haas (1969)
Diplodon (Rhipidodonta) variabilis — Bonetto (1965), Figueiras (1965)
Diplodon variabilis — Parodiz (1968)
Rhipidodonta variabilis — Simone (2006)

Unio subtrapezius Philippi, 1847
Philippi, 1847. Z. Malak. 4: 96.
Philippi, 1848. Abbild. Beschr. Conch. 3: 80, pl. 5, fig. 3.

Glabaris (s.s.) membranaceus — Simpson (1900)
Anodontites (s.s.) membranaceus — Simpson (1914)
Lampsilis (Cyrtonaias) saladoensis — Frierson (1927)
Diplodon variabilis — Parodiz (1968)
— Haas (1969)

Unio bulloides Lea, 1859
Lea, 1859. Proc. Acad. Nat. Sci. 11: 187.
Lea, 1860. Jour. Acad. Nat. Sci. 4 [O. 7]: 264 [82], pl. 42, fig. 144.
Type(s): HOLOTYPE USNM_85776, Rio de la Plata, S.A.

Diplodon (Cyclomya sec. Bulloideus) bulloides — Simpson (1900), Simpson (1914)
Diplodon (Bulloideus) variabilis — Haas (1931), Thiele (1934), Haas (1969)
Diplodon bulloides — Bonetto (1959)
Diplodon (Rhipidodonta) variabilis — Bonetto (1965), Figueiras (1965)
Diplodon variabilis — Parodiz (1968)
Diplodon (Bulloideus) bulloides — Haas (1969)
Rhipidodonta variabilis — Simone (2006)

Unio locellus Lea, 1866
Lea, 1866. Proc. Acad. Nat. Sci. 18: 34.
Lea, 1868. Jour. Acad. Nat. Sci. 6 [O. 12]: 264, pl. 33, fig. 79.
Type(s): HOLOTYPE USNM_85189, Buenos Ayres, Argentina.

Diplodon (s.s.) locellus — Simpson (1900), Simpson (1914)
Diplodon delodontus wymanii — Haas (1930)
Diplodon (Rhipidodonta) variabilis — Bonetto (1965), Figueiras (1965)
Diplodon burroughianus burroughianus — Parodiz (1968)
Diplodon (s.s.) delodontus wymanii — Haas (1969)
Diplodon burroughianus — Mansur (1970)
Rhipidodonta variabilis — Simone (2006)

Diplodon subquadratus Marshall, 1922
Marshall, 1922. Proc. U.S. Nat. Mus. 61(2437): 3, pl. 2, figs. 6, 8; pl. 3, figs. 8-10.
Type(s): HOLOTYPE (ORIG. DESIG.) USNM_335774, Paysandu, Uruguay.

Diplodon subquadratus — Marshall (1922)
Diplodon (Cyclomya) paranensis funebralis — Haas (1931)
Diplodon subcuadratus [sic] — Bonetto (1959)
Diplodon (Rhipidodonta) variabilis — Bonetto (1965), Figueiras (1965)
Diplodon variabilis — Parodiz (1968)
Diplodon (Rhipidodonta) paranensis funebralis — Haas (1969)
Rhipidodonta variabilis — Simone (2006)

Unio membranacea Hanley, 1843
Hanley, 1843. Illustr. Descr. Cat. Rec. Bivalve Shells: 202, pl. 22, fig. 6.
(reference to Mytilus membranacea Maton, 1811)

Glabaris (s.s.) membranaceus — Simpson (1900)
Diplodon (Cyclomya sec. Bulloideus) variabilis — Simpson (1900), Simpson (1914)
Anodontites (s.s.) membranaceus — Simpson (1914)
Diplodon (Bulloideus) variabilis — Haas (1931), Haas (1969)
Diplodon (Rhipidodonta) variabilis — Bonetto (1965), Figueiras (1965)
Diplodon variabilis — Parodiz (1968)
Rhipidodonta variabilis — Simone (2006)

Mya variavilis Corsi, 1900
‘Matón’ Corsi, 1900. Anais Mus. Nac. Montevideo 2: 448.
(error for Mya variabilis Maton, 1811)

Diplodon subcuadratus Bonetto, 1959
‘Marshall’ Bonetto, 1959. unknown publication: 55.
‘Marshall’ Bonetto, 1965. Anais Congr. Lat.-Amer. Zool. 2: 47.
(error for Diplodon subquadratus Marshall, 1922)