Attached scenario2 is basically the same as scenario1 from the previous post.
The only difference is the addition of a solid cylindrical mass 'V' which is suspended above and which loosely fits in container 'B'

Containers 'A' and 'B' and the solid cylindrical masses 'M' and 'V' could be constructed from clear acrylic with a specific density of 1.19 in which case the fluid could be a salt water solution with the same density of 1.19   

Attached scenario4 starts with the ending position 5A/5B from scenario3.

Mass 'V' remains in the same position. Container 'A' moves upwards and container 'B' moves downwards.

Each position is at equilibrium as a result of the counterweights on the pulley. As a result a small force on the left side of the pulley will transition 5A/5B anti clockwise to 6A/6B and 7A/7B

Mass 'M' is 'pulled up' against gravity untill no longer submerged (which is cancelling out the positive gravitational force from scenario2 where mass 'M' was submerged in container 'A' )

Attached scenario6 starts with the ending position 9A/9B of the previous scenario5

As per the red arrow mass 'M' has gained potential gravitational energy which should be sufficient for the forces needed to transition from position 1A/1B to 9A/9B (which are all at equilibrium).
We now return to the starting position 1A/1B

Since I do not believe perpetual motion based on gravity/buoyancy is possible there must be a (probably simple) mistake in this design.

From those of you who take the time to analyse this (which is relatively easy to replicate in Excel) I hope to receive constructive feedback. In addition please feel free to ask questions on anything which may not be clear.

For now I will not elaborate on the forces which keep the portion of 'V' which is not submerged in balance since I believe the error must be in the parts of the design I have explained so far.

@ Tarsier_79

"As you displace more water, your water acts as if it is pushing against the displacement.... I am sure you know how it works. eg. 7B will try to push down. When this happens, 7a will rise, dropping the relative water weight, until it looks more like 8a and 8b.

So your counter-weight not only has to compensate for the difference in weight change, but also water changing levels , again changing the weight."

Can you have a look at attached file (not sure how to insert the file as part of the text like you did...);

A counter weight 1C is attached via a string on a pulley with twice the distance as mass 'V'
Therefore only half the weight is required to keep 'V' and 1C at equilibrium.

The orange part of mass 'V' is submerged in 2B.
Since the density of mass 'V' is equal to the density of the fluid the submerged part will float and not exert any up- or downward force.
The part of mass 'V' above the surface is balanced by the weight of 2C

Both scenario's 1 and 2 are at equilibrium.
Any in between stages between the transition from scenario 1 to scenario 2 should be at equilibrium as well.

As a result a small additional weight added to 'V' should be able to complete the transition.

Can you let me know if you believe above statements are incorrect or if you believe this is a different scenario then 7A and 7B.

"Fact: you can't get anything for nothing in a gravity system."

I totally agree.

PS - not sure how to insert your text as quotes with my reply...

How does D move up and down to compensate?

The rest makes sense.

As soon as you add the second set of pulleys so the containers move up and down it adds another level of complication.

Everything you have drawn is easy enough to reproduce if you have the will to do so.

Here is a link to one of my last buoyancy tests.
https://www.besslerwheel.com/forum/viewtopic.php?p=177387#p177387
I have attached a pic below.

I then up-scaled the principle to a new model

I shouldn't have said buoyancy, more displacement.

You can make your structures out of layers of polycarb, don't use acrylic, because it will crack if you are not used to it. Glue them together with super glue. It is clear, so you can trace the shape from an enlarged graph paper model or printout. Clear tubing is cheap from the hardware store, as are fittings designed for irrigation. You can use the same method to build your pulleys. Alternatively if you are more computer savvy, you can get all or some of the parts 3d printed.

If you can simplify your principle to build a simple test jig, that may give you the answer you are looking for.