Engineering undergrad versus grad school

Seeking info about engineering in college, as an undergrad major versus graduate program. I have heard of ABET accreditation for undergrad programs. Does this exist at the grad level? Is it unusual for STEM majors (not in engineering) to attend grad school in engineering.

Or better way to ask: can a student without an undergraduate ABET accredited engineering degree go to grad school and get ABET accreditation? If yes, would it be possible with an M.S. degree or would the PhD be necessary? And at that level, is the ABET accreditation relevant?

Current thinking is an undergraduate degree in engineering physics which does not come with the accreditation. Grad school maybe aerospace but possibly some other type of engineering.

ABET accredits a few MS programs but it’s a very unimportant thing at the graduate level. Most major programs don’t bother.

Graduate school is fairly common but not necessary for engineers. Also, an engineer should never pay for their own graduate school: have an employer do it or a fellowship or an assistantship.

Most of the ABET masters programs are in Occupational Health. There’s too much variability in the rest of the graduate programs to stamp a standard on it.

@boneh3ad would know better, but I would think a non-ABET UG degree might be an impediment to getting into a graduate program. It can certainly limit job choices, especially for engineers that need a PE.