Hi Donna -
I have an L made of two Linmon table tops with an Alex at each far end and legs where they meet - what you don't want. : ) If I had added more Alexes there wouldn't be room for my legs. I have a larger (not largest) and a medium Linmon. Here's the largest:
LINNMON Table top - white - IKEA
And all of the Linmons:
http://www.ikea.com/us/en/search/?query=Linmon
With two of the largest, you could have four Alexes but would need to measure to see if you could have more. And would you want to? You couldn't roll a chair right up to an Alex if there wasn't a knee hole.
I put a third Alex to the right of my L. To protect the tops I had a glass company cut 1/4" plexiglass to size and polish the edges, with small, absolutely flat "bump-ons" they give out by the handful underneath so the tops wouldn't slide around the desk. Prices varied hugely. (I like plexi better than glass - warmer if my arm is on it plus not as loud if I put something hard on it.)
For example, this is the largest Linmon, which I have as the main part of my L:
LINNMON Table top - white - IKEA
You'll just need to measure your space and what room you'll need for a chair and you before purchasing. But the idea makes total sense.
On a different wall I have a Linmon top with Ikea's expandable legs for two trimmers. I cut better standing up (I'm short) but bending over hurt my back. So I did a cutting motion while my husband measured where my hands/arms were. Like air guitar. ; )
Clear as mud and not specific enough, right?