Theodore's descendants, the Palaeologus-Montferrat family, ruled at Montferrat until the 16th century, though they were sometimes given Greek names, such as Theodore and Sophia, most of the Palaiologan Marquises of Montferrat paid little attention to affairs in the eastern Mediterranean. The only Marquis to seriously consider using his Byzantine connection was Theodore's son, John II of Montferrat, who wished to take advantage of the Byzantine civil war of 1341–1347, between Andronikos II's great-grandson John V and John VI Kantakouzenos, in order to invade the empire and conquer Thessaloniki. In his will from 1372, John II claimed that Andronikos II's deposition in 1328 by his grandson Andronikos III (John V's father) had been unlawful and thus disqualified Andronikos III and all his heirs from the legitimate line of succession to the throne of Byzantium. John II also pointed out that since Andronikos II had disinherited Andronikos III, John II was thus the rightful emperor as the only true heir to Andronikos II. John II even petitioned the Papacy to recognize his claims to Thessaloniki and to the empire, and to help him conquer them. An expedition to "recover" these territories was never organized.