My kid was studying for the ISEE (because that’s what most private day schools near us require) in 8th grade. When we broadened our search to include boarding schools and discovered that those mostly required SSAT, I called AOs at some of the schools to ask if my kid would need to take both. Most schools were willing to take either even if they didn’t mention it on their website.
That being said, kid ended up taking SSAT and asking the ISEE schools to use that score instead.