Margaret,
Here is what I know about the sons of Tomé Raposo (who died before 1734) and Sebastiana da Costa. In the marriage record of their son António it says that Tomé and Sebastiana were from Arrifes:
Antonio Raposo married Vitoria Cordeiro, daughter of Bartolomeu Afonso Sardinha and Teresa Ferreira in Relva, 1721. Since men used to first marry at 25, let's take 1696 as his probable year of birth. Vitoria died and Antonio married Maria de São José, who was the daughter of Manuel de Teves, of S. Antonio Além Capelas, and Maria de Souza, of S. José - Ponta Delgada, where the marriage took place in 1744.
Pedro Raposo, christened in Patriarch S. José, married Antonia de Souza, christened in S. Sebastião, Ponta Delgada, daughter of André de Souza and Luzia de Almeida, in S. Sebastião, Ponta Delgada, 1734. Supposing Pedro to be 25 then, he should have been born around 1709.
Gonçalo Raposo, christened in S. José, Ponta Delgada, married Maria Pereira, of Bretanha, daughter of José Carvalho and Maria Pereira, in S. Antonio Além Capelas in 1735. It's reasonable to suppose he was born by 1710.
Silvestre Raposo, christened in S. José, Ponta Delgada, married Joana Botelho, daughter of Amaro Botelho and Francisca Pacheco in S. Antonio Além Capelas 1n 1739. Let's assume Silvestre was born in 1714. After her death, he married Bárbara Medeiros, christened in S. Antonio Além Capelas , daughter of Domingos de Souza and Teresa da Costa, in 1743, in that same parish.
Except for my gggggfather Pedro, all the above information is the result of a research by John Miranda Raposo.
Hope you will come across something. If you Raposos are from Arrifes, as mine, there should be a connection somehow.
Thank you, so much,
Marcos.
P.S. - I've checked the Almanak Laemmert of Rio de Janeiro from 1880 to 1889 in quest for your José Pimentel, who arived here in 1880. Unfortunately, he was not be found. That doesn't mean he wasn't here, it only means he did not hold a position of visibility yet.