Here I've found the 1905 NYS Census record of the Mulvaney family at 270 Van Brunt St. The family is listed as Patrick, 45; Julia, 37; James, 11; Grace, 9; Mary, 8; William, 5; Thomas, 3; Raymond, 1; and Harold, 6 months old. There are also 2 "boarders," who are their nephews, 17-year-old John Murphy and 11-year-old Thomas Murphy.
What's new here is Raymond. Betty and John had mentioned that they thought there might have been a brother named Raymond who died as a toddler. Never having seen any evidence thereof, I was skeptical. However, it appears that little Raymond did exist, and that he lived at least 15 months. (Harold is 6 months old. Do the math.) As per usual, Patrick is a Machinist and Julia does the housework. Nephew John, at 17, is an office boy, while Thomas, at 11, is in the 4th grade. Patrick and Julia's older children, too, were in school. James, also 11, was also in the 4th grade. They might have been best friends, classmates, or both! Though the number next to Grace looks like a 5, I assume it was just a sloppy 3, and that she was in the 3rd grade, where she should have been. Mary - Auntie Mae - is in first grade.
I was honestly not expecting a lot of new information from these census records. The Mulcahys were nice but not particularly important. The Mulvaneys, on the other hand, are chock full of new things and clarifications. Raymond existed. Good to know. The Murphy brothers lived with the Mulvaneys for at least 5 years. Their parents probably died between the 1900 Federal Census and the 1905 NYS Census. That's important information.