If you wanted to boost up a club to take on the Big 3, then Braga would be it, bit they are under the Qatari umbrella already
Other options (besides Boavista (2001) and Belenenses (1946), who are the only 2 non Big clubs to have won the topflight league) would be Vitória Futebol Clube, from Setúbal, a suburb of Lisbon, Académica de Coimbra (Coimbra), who have collapsed, down the the third tier, Vitória de Guimarães (Guimarães), G.D. Estoril Praia (who you already mentioned), Rio Ave Futebol Clube (Via do Conde), F.C. Paços de Ferreira (Porto area), Gil Vicente F.C.(Barcelos, near Braga), Sporting Clube Farense (Faro in the Algarve), and Marítimo da Madeira, based in Funchal, on the island of Madeira.