"Getting some rest" and "taking a nap" are two of the most common phrases that can be used as synonyms for "catch some shuteye". "Snoozing", "dozing" and "napping" can also be used interchangeably with this phrase. If you're looking for a more casual way to express that you're going to sleep for a short period, you can use slang terms such as "taking a power nap", "slipping into dreamland" or "having a siesta". "Recharging your batteries" and "refreshing your mind and body" can also be used to convey the idea of catching some shuteye. Whatever the term you use, remember that it's essential to prioritize sufficient and quality sleep to maintain optimal physical and mental health.