IMO you have lots of options as you have mentioned:
1. Drill 6â into the slab to add rebar steel for the extension using concrete on one side.
2. Frame up and out on the existing slab with shelves above and extending on each side.
3. Add Treated 2X material on concrete blocks drilled and anchored to existing slab.
This could go on and on at this size with options since this appears light storage. Your Choice!

If this is an old existing slab, you it may be best to place the new shed on a 2 X frame that is on blocks that sits on the slab.

This assumes that the existing slab is at or slightly below the surrounding ground. If if is lower, the water from the surrounding area will end up in the new shed. creating mold and other water problems.

With the shed raised from the existing slab, there will be no vegetation growing under the shed. By keeping it open on all four sides there will be little protection for animal nest.

My shed is not on a slab but on blocks and is 10 X 12'. It is about 10' on the average above the ground level I have hid the opening under the shed with plantings, and use two 2X8 as a ramp to get my equipment in and out.

loger: I am skeptical about being able to drill into the existing slab. It is 30+ years old and well cured. The slab is about 4-5" above grade, so I also do not want to build it up any more than I have to. Didn't get the part about "shelves on each side". Is that to avoid any load on the cantilevered part of the floor?

So, it sounds like the best option is to frame the floor with treated 2x's over the existing slab and extend the floor frame a foot on each side. Still feel like I need some footing below each corner. Could I go down 24", pour a pad and then use a treated 4x4's as posts, leveled with the top of the slab, and fill the holes with pea gravel?

This is a 48'x80' shed that I am building. I am just using it to give you a visual idea of what you could do with the existing pad.

If you wish to use the pad but make the shed larger than 6x10. Say 10x12 for example. Dig down below the surface of the outer edges of the pad (much like digging a ditch) to the desired size.

Measure and set the post to the size shed you want.

On the bottom outside of the post nail 2X's (4,6 etc) so that they are level with the pad. Then fill the void with gravel base and then concrete to make the entire pad level.

Build the shed. You can go back later and paint the pad which is now your floor to make the finish even between old and new construction.

Once I have the roof finished on my shed. I will go back and remove the grass and run a compactor over the surface. Lay a bed of compacted gravel over that. Then nail 2"x6"'s level around the outside of the post. and pour the concrete using them as forms.

The yellow triangles are to show how this will be done. This does a few things. It allows me to drill the post and run rebar rods through them to covered with concrete. Makes the walls even with the outside stringer. Places the siding out away from the concrete pad 1 1/2" for drainage (stringer will be even with the pad making it weather proof). Adds another 6 inches of support to the corner post on two sides and three on the side wall post.

Just an Idea of my way of building sheds for you to consider.

I mentioned shelves because It appears that you only need a small shed for storage vs extreme wt. I see no problem with 1â of shelving extending on ea side with treated materials. Attaching two extensions onto the slap using a hammer drill and 3/8â anchor bolts and 3 concrete blocks along outer edges would be the less expensive IMO.

Mixing/adding that small amount of concrete to attached rebar steel might be your best option X Less All Etc.

OR! Frame on the concrete just for the shelves/walls/ext flooring only (2X4 treated plates X 4 ext walls above floor, 2X walls, ply floor, concrete blocks under extension and Etc needs). OR! Extend the floor and add a planned Rubbermaid Shed to the floor.

Adding a complete treated floor on the slab is an option with more added cost. This is a small project with lots of options. Please post a Pic of the slab.

Here's a pic of the pad:

Thanks! My vote is to add Home Depot's Extra Strength concrete with 3/8" rebar steel 24â o.c. extended into the existing pad/slab. Or! Frame directly over the pad. Good Luck!

OP... I have exactly the same problem as you! I'm in California. What did you end up deciding? Slab addition, rebar'ed into existing slab? Or two new concrete piers/footings, with the floor of the shed overhanding from the old slab to the piers?

Sorry, I can't help. It was my son's house and he ended up selling before we could do anything about it. If you are in California and not in the mountains, you really don't need to worry about freezing and heaving. I would just use the existing pad, use concrete blocks to extend the pad and frame a floor over both.