I've found it easier to divide the clump rather than try to separate individual plants.

I thought I had 'updated' this post, but obviously I didn't do it correctly...
Additional plants are growing from the side of the mother plant so when removed there is no roots.
And some of the 'clumps' are huge with 20+ palms in the space.

They are at least 5 or 6 mts. tall, in the garden

Yes, at that size you wouldn't want to be trying to divide the clumps. Mine don't sucker that high on the trunks, that is starting to look more like branching. I've heard that there are about 40 varieties of these so maybe it's a characteristic of the one you have. I wouldn't consider that clump as large, in the sense of broad. Mine of that size are large as well. My tallest variety have few trunks but seed prolifically. So there's hundreds of seedlings coming up around them. That tends to be a nuisance.

About the only thing I could suggest for those is to trim the fronds off and use a rooting powder. If you keep it all sterile then perhaps you might get roots before any rots set in. Good luck with it.

Thank you. We will try, again....
There are larger/bigger/wider clumps, but the ones in the photo, are closer to the house 8-)
There isn't many seedlings though, but some of other varieties we have, is a different story.