Common suffixes:
* -ful: caring, careful (meaning full of care)
* -less: careless (meaning without care)
* -er: carer (meaning someone who provides care)
* -ing: caring (meaning the act of showing care)
* -ed: cared (meaning past tense of care)
* -s: cares (meaning plural of care, or present tense of care)
Less common, but possible suffixes:
* -ingly: careingly (meaning in a caring way)
* -ness: carelessness (meaning the state of not caring)
* -ive: (not usually used with "care")
* -able: (not usually used with "care")
The best suffix to use depends on the specific meaning you want to convey.