It is possible, especially if your ALEXANDER family is Jewish. My great-grandfather Mor ALEXANDER and his wife Ilona ROSENBAUM lived in Bekescaba while they had their children and later his son Laszlo lived in Budapest, but I do not know if he had a wife before Ilona or if Mor lived previously in Budapest.
I do know that he was born around 1874 in Szarvas and died in the 1917/8 flu epidemic. Possibly, Mor's parents were Zsigmond ALEXANDER (b. 1844) and Rebeka SCHWARTZ (b. 1851), but I haven't fully confirmed that.
At the very least, we might be cousins, Ilonka!