That actually sounds like a pretty good idea and ought to help increase your growing area. I guess the only issue would be that since you are growing more plants, you might need to top off your reservoir a little more frequently and/or change your nutrients.

That's what this guy was doing
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He used to post here but hasn't in a long time. I'm not sure he was using NFT, the picture looks more like a modified flood and drain, but you can clearly see the 'kiddie pool' he has using as a res on the right side with plants floating on it.
If you search the forum for "hotpepperclub" (maybe with spaces)you may find some of his posts. That's in the name of his website and he always posted links.

Now please look at what it takes to produce using Aquaculture even on a small scale. You'd have to depend on to many outside thing to keep this kind of operation going. In the 1960 maybe this system would look nice but in this day and age get real. There'swso many learning curves you have to get over even to begin. This is one of those things you can only do with excess. Yes it's a great system, yes it produces. But there's too many but's today to make it work sustainably.

you should check out his site goergeiii, he has indepth details on making sustainable system. In summary, he makes a filter bag out of landscape fabric fills it with dirt and suspends it in a sterlite/rubbermaid tub with water in the bottom. he adds water and nutrients through a pipe in the top.
It's a nice repeatable design that doesn't require ph or ec measurements.