During the two-month period of late March to early June, 1837 Howard Vyse blasted entries into the four unkown voids above the King Chamber in the Great Pyramid. On August 6, two months later, he wrote in a foot-note about a cartouche of Menkaure that it was not alike those of his predecessors Suphis I and II. Therefore, Howard Vyse, at this time, still believed that Suphis I and II were two different rulers. He used the word "predecessors" not "predecessor"!
The idea that Suphis I and II were different rulers came from a tomb nearby, G6020 built during the Fifth Dynasty. This mastaba was called "16" by Lepsius and the "Tomb of Trades" because of the stunning reliefs in vivid color showing the various crafts of Egyptian life. I was in this tomb in May of 2019. One photo in particular explains why the idea of two separate rulers may have arisen.
Here, Khnum-Khuf can be seen nestled among Sahura, Nefer-ka-ra, and Shepses-ka-f. Elsewhere in the tomb, the cartouche of Khufu is inscribed. Since the names appear similar yet in such different contexts, it makes sense that early explorers may have thought that Khnum-khu-f and Khufu are two distinct names designating two different rulers, possibly related as father and son or brothers, Howard Vyse included. However, both names appear on graffiti inside the relieving chambers, at the entrance to a Sinai Peninsula mine, and on the Papyri Wadi El-Jarf suggesting that they were two alternative names of Khufu/Cheops, not two distinct rulers, Saophis (Suphis I) and Sensaophis (Brother-of-Suphis, Suphis II) as proposed by Eratosthenes over two thousand years later.