That's if you limit them to one stem and train them up a trellis.

The problem with this is a limit in the number of fruit you can set

Tomato spacing is a very common topic in this forum. A search will find numerous hits and more opinions than you can count, but most of them say pretty much what ribbit sez. Closer spacing: more work.

Dan

Agreed. You may or may not get more tomatoes per sf, but it's a heck of a lot of work planting them 1 per sf then keeping them pruned back to 1 vine and tying them up a stake. I spaced mine 3 1/2 feet apart and just let them go wild except for trimming off the leaves that touch the ground and occasionally where the leaves are all matted together in a clump. Even with that much space they've already turned into a tomato hedge 5-6 feet tall. The only real advantage I can think of is the ability to try a bunch of different varieties in a small space.

I think that the average is 2sq feet around here, unless they live in a more arid climate and can get away with 18". The big problem with being too close is that when it gets wet, it doesn't dry out and then disease can take hold. So you need the right balance of airflow to dry out the plant, sunlight for the leaves, and some shade for the actual fruits.
Hope that helps,
Susan