I've never grown more than two tomato plants per net cup, though I don't see why it wouldn't work provided the roots all get enough moisture and you're able to spread the stems out enough for them all to grow.
If you see one isn't fairing as well as the others you could always cut it out later.

Thats always a tough choice for me because I hate thinning but you are using hydroponics and the idea is to have the best of the best possible. Thinning out the weaker plants leaves you with the strongest genetically.

Your biggest concern is crowding

You may have problems with fungus and disease if there is not enough air flow. Lots of roots too, that will need extra moisture and nutrient and oxygen Lots of roots can slow things down.

Here is a link that might be useful: alternative-innovation.com

I listen to the experienced ones, I trimmed to 2 plants each. Thanks....

Having grown like 5 tomato gardens from AeroGrow..until I found my own tomato seeds and now grow my own type that I like. IF you grow more than 3 tomato plants, you cut down on the tomatos you will get. The plats get big....if you dont prune them heavily, you can fill the garden with the 3 tomato plants. Like I posted for another grower here...plant some herbs in the empty growplug holes, if you have the baskets to grow them in. OR try growing the Micro Tom tomato. You can grow 7 plants! They are only 4-7in high,of course, and you only get tiny tiny tomatos, about the size of a pea. BUT you use the entire garden and they taste pretty good in a salad...or as you walk by, you pick one off and pop it in your mouth! They are fun to grow and kids learn to grow vegetables. And you get fruit in like 3-5 weeks! I have 3 growing now and all are blooming and fruiting. Just waiting for them to ripen. Under the lights they are taller than when grown in soil and outside, and teh tomatos are a bit bigger. BUT they are the worlds smallest tomato. So dont expect a beefstake tomato:) But the one that comes from AeroGrow are small and they are ok..but this is an option. They have a more tomato taste to them,you just have to grow more of them. and you can!

BUT if you stick with the Aerogrow tomatos,...grow only 3 plants,...they will get 'big',..and the system will only grow 3 great plants...or 4-6 so so plants,you choose So...grow something else. like the Micro Tom tomato...or other dwarf tomatos. IF you are set on tomatos. Or grow your own garden of your choice, that will fit under the lights...dwarf plants. Buy the seeds and check the heights. then grow what YOU like, remember to pick the right setting on the garden for what you are growing, to get the right light timing.