Its' hard to picture from the description...I am no contractor but I never heard of laying the joists flat...how would you do the blocking...anyway I inserted a link I found about using 2 x 4...

https://plasticinehouse.com/can-you-use-2x4-for-deck-joists/#:~:text=You%20can%20use%202%C3%97,your%20guidelines%20for%20safe%20construction.

On the patio, the 2 x 4s would be laying flat on the concrete patio, with spacers every 12” or so. the alternative is to put the 2 x 4’s on edge, making the deck surface 2” higher. I’ve read of other people doing it with 2 x 4s laying flat. I can’t see any reason why laying them flat would be a problem, because the 2 x 4’s are never spanning more than 12” between supports (less, actually, since the spacers would be 12” OC).

The problem is the part of the deck that would extend beyond the patio. The ground surface is currently just a bit below the patio surface, sloping away from the patio. At the point that would be the edge of the deck, the ground surface is about 4” below the patio surface.

The only way I can think of continuing the deck beyond the patio at the same level is to use most buried concrete blocks, which would also have to be very close so that the 2 x 4’s are not spanning much between blocks. But that’s a lot of blocks!

I’m thinking I might just have to give up on a deck…

Ok I kinda see. The patio supports the 2 x 4. Just extend the patio. I saw on some website, they sell "deck tiles" that you just can lay over patios. Seem to look nice. Maybe check it out. As far as giving up...I am working on figuring out how to attach deck boards as rails to my deck posts...all brackets I see are 1.5 inch vs 1 inch what I need. But...I will never give up :>)

Thanks for the idea. It’s a choice between a deck and some sort of paver-style surface. If I used blocks to support the 2 x 4s beyond the patio, I’d sort of be extending the patio. I’m warming up to that idea. :)

Wood decks are for raised-level access. Concrete, brick, stone, and pavers are for grade-level access. Add to that you don't even like the footprint of your existing patio.

You can't force a system that is not appropriate and not expect problems. In other threads, sharp-tongued commenters always suggest selling the house and buying what you really want rather than force something that doesn't work.

Well, decks have aesthetic appeal, also. Function isn’t everything. Can you tell me why it wouldn’t work?

Water and moisture. Roof, if existing, doesn't cover the sides or the end sticking out. No air movement, cupping, curling, early rot. Accumulation of dirt/debris close underneath promoting the aforementioned. Fastening solidly with only spacers to adjust for the slope.

It seems to me that "low decks" which function like a patio are built where there was no patio before...maybe they want the options that come with wood like built in benches etc...close to the ground..or touching...I would always go with concrete. If you wanna dress it up...blocks and brick...you can get some really nice...and long lasting beauty...with those materials...Wood close to the ground...unless PT or some sort of tropical hard wood...eventually will have issues..and will be hard to maintain I think.

Those are good points. I was thinking I might have to give up on a deck Seems that is the case Well, pavers can be cool. Thanks to both of you for your comments!

I had this weird area under my deck but above my car port...the car port is concrete block but had a sill plate over the blocks for the wooden carport cover...anyway...after years of getting wet it got rotten and was falling apart...I hired a guy to replace it...dig it out and put a new one....he took one look and said "why don't you just use concrete?"...and I said "really..u can do that?"...so he did it....best decision i ever made in that regard...its rock solid...and no rot...

Agree about decks looking good, no doubt when composite is used. Check into porcelain pavers, some are pretty wow. Sounds whatever you choose the slab might be coming out. Especially if you have to build a roof it needs footings anyway.