Probably, but ... why ... whyyyy ... whyyyyyyy?!
If you replace the original 16 GB SD-Card with a new one, it costs like ... uhm .. "nothing"?!
Of course, you can also use a bigger SD-Card, 32, 64, 128 .. whatever, but makes not realy sense to me. If you want to save up or backup videos, you need to save it to your mobile phone anyway (currently) and can then move it whereever you want. Else it will get overwritten sometime. No matter if 16 or 128 GB. And again: 16 GB will handle several thousand videos already, who needs more? And write speeds?! Serious? Ever checked what video codec eufy homebase uses to save the files and how big they are? You could even "slow down" the current original 16 GB sd card to the half of its speed and it probabl will still be enough for the eufy homebase So writing speed is soooo much unimportant in this case. (Except you would have plenty of cams running at the same time and all of them would frequently and simultaneously would write data, then ok)
The eufy homebase probably will also handle 256 GB or even 512 GB sd-cards, even if not officialy supported. You just need to try it! ... I got a PVR which only officialy supports up to 32 GB SD-Cards and i am running a 128 GB SD-Card with it since years without a problem. Only testing it will let you know if it works, or fails. But again: For this case (eufy homebase and cams) 512 GB would be like shooting for sparrows with cannons! A 512 GB SD-Card would handle close to 100K videos ... insane