Claiming mother but can father also file jointly with her?

Hello,

 

I have been supporting my mother through the pandemic as she was not working. She has $0 income for 2020. If I claim her as my dependent, should my father also file jointly with my mother or should my father file married but single? What would be the pros and cons for him to file either way? I would be unable to claim my father as his income is above the $4,000 limit. Thank you in advance!