The short answer is: Yes, you can open the bottles, dump into a container, re-sanitize the bottles, and filter back into the bottle. You'll want to add more sulfites and be very careful about oxidation. Not sure what equipment you have for filtration. If it is bacterial in nature, you'd need to put it through a 0.45um filter to completely remove it.
The longer answer involves determining what the floaters are and addressing the root cause. If it is some spoilage growth, then the wine may already be compromised and you'd need to evaluate your sanitation regimen for next time. If they were there during bottling and were drawn into the bottles, then an additional aging+racking next time will prevent this.
Perhaps rather than re-bottling, it may be time to share with friends and screen filter on the way to their glasses!
Cheers!