A method for polymerizing polydiorganosiloxanes comprising: 1) heating, at a temperature of 50°C to 150°C, a reaction mixture prepared by mixing starting materials comprising A) a polydiorganosiloxane of average unit formula [ R2SiO1/2]2(R2SiO2/2) n, where subscript n is 0 to 2000, and each R is an independently selected monovalent hydrocarbon group of 1 to 18 carbon atoms; and B) a catalyst, at a concentration of 0.001 to 0.01 mol/L based on amount of starting material A), where the catalyst comprises B1) a salt -anion complex selected from the group consisting of B1i) a quaternary ammonium - fluorinated carboxylate complex, B1ii) a quaternary ammonium - sulfonate complex, B1iii) a quaternary phosphonium - fluorinated carboxylate complex, B1iv) a quaternary phosphonium - sulfonate complex, B1v) an imidazolium - fluorinated carboxylate complex, and B1vi) an imidazolium - sulfonate complex; B2) an acid selected from the group consisting of a fluorinated carboxylic acid and a sulfonic acid; thereby preparing a reaction mixture; where B2) is used in an amount of 1.5 moles to 10 moles per mole of starting material B1); and 2) recovering a product from the reaction mixture, where the product has unit formula [ R2SiO1/2]2(R2SiO2/2) m, where m > n. 1) heating, at a temperature of 50°C to 150°C, a reaction mixture prepared by mixing starting materials comprising A) a polydiorganosiloxane of average unit formula [ R2SiO1/2]2(R2SiO2/2) n, where subscript n is 0 to 2000, and each R is an independently selected monovalent hydrocarbon group of 1 to 18 carbon atoms; and B) a catalyst, at a concentration of 0.001 to 0.01 mol/L based on amount of starting material A), where the catalyst comprises B1) a salt -anion complex selected from the group consisting of B1i) a quaternary ammonium - fluorinated carboxylate complex, B1ii) a quaternary ammonium - sulfonate complex, B1iii) a quaternary phosphonium - fluorinated carboxylate complex, B1iv) a quaternary phosphonium - sulfonate complex, B1v) an imidazolium - fluorinated carboxylate complex, and B1vi) an imidazolium - sulfonate complex; B2) an acid selected from the group consisting of a fluorinated carboxylic acid and a sulfonic acid; thereby preparing a reaction mixture; where B2) is used in an amount of 1.5 moles to 10 moles per mole of starting material B1); and A) a polydiorganosiloxane of average unit formula [ R2SiO1/2]2(R2SiO2/2) n, where subscript n is 0 to 2000, and each R is an independently selected monovalent hydrocarbon group of 1 to 18 carbon atoms; and B) a catalyst, at a concentration of 0.001 to 0.01 mol/L based on amount of starting material A), where the catalyst comprises B1) a salt -anion complex selected from the group consisting of B1i) a quaternary ammonium - fluorinated carboxylate complex, B1ii) a quaternary ammonium - sulfonate complex, B1iii) a quaternary phosphonium - fluorinated carboxylate complex, B1iv) a quaternary phosphonium - sulfonate complex, B1v) an imidazolium - fluorinated carboxylate complex, and B1vi) an imidazolium - sulfonate complex; B2) an acid selected from the group consisting of a fluorinated carboxylic acid and a sulfonic acid; thereby preparing a reaction mixture; where B2) is used in an amount of 1.5 moles to 10 moles per mole of starting material B1); and B1) a salt -anion complex selected from the group consisting of B1i) a quaternary ammonium - fluorinated carboxylate complex, B1ii) a quaternary ammonium - sulfonate complex, B1iii) a quaternary phosphonium - fluorinated carboxylate complex, B1iv) a quaternary phosphonium - sulfonate complex, B1v) an imidazolium - fluorinated carboxylate complex, and B1vi) an imidazolium - sulfonate complex; B1i) a quaternary ammonium - fluorinated carboxylate complex, B1ii) a quaternary ammonium - sulfonate complex, B1iii) a quaternary phosphonium - fluorinated carboxylate complex, B1iv) a quaternary phosphonium - sulfonate complex, B1v) an imidazolium - fluorinated carboxylate complex, and B1vi) an imidazolium - sulfonate complex; B2) an acid selected from the group consisting of a fluorinated carboxylic acid and a sulfonic acid; thereby preparing a reaction mixture; where B2) is used in an amount of 1.5 moles to 10 moles per mole of starting material B1); and 2) recovering a product from the reaction mixture, where the product has unit formula [ R2SiO1/2]2(R2SiO2/2) m, where m > n.