24 quarter units = 16 semester units. For UC transfer purposes, your non-UC lower division units (from community colleges) would be capped at 70 semester units (however, all courses count for subject credit). Adding 16 semester units from UC would mean that you have 86 semester units for the purpose of transferring to a different UC.
https://www.ucdavis.edu/sites/default/files/upload/files/f17tip_unitlimits.pdf suggests that 86 semester units may cause problems if you try to transfer to UCD or UCM (80 semester unit limit) and just barely avoids trouble at UCLA (86.5 semester unit limit). However, the document is a few years old, so you may want to ask each campus of interest directly if you want to transfer to a different UC.
CSU policies may be different.