Pressure wouldn’t suspend it.
Instead, the object would sink until it encounters a fluid that is denser than that object, at which point it could be suspended by buoyancy (i.e. it would float on top of the denser fluids).
This broadly doesn’t happen in Earth’s oceans because water is functionally incompressible, and thus the density of the water wouldn’t really change as you get deeper (e.g. at the bottom of the Mariana Trench, sea water is only about 5% more dense than at sea level). You could do it with an object just *barely* more dense than water (at sea level). Alternatively, you could do it above a brine pool on the ocean floor, with an object denser than water but less dense than the brine (which is about 25% more dense than normal seawater).
You also would get this effect in other fluids that are more compressible (e.g. gases).
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