Earth's deepest point, the Challenger Deep, is almost seven miles below sea level. By contrast, Europa is smaller than even Earth's moon, yet its oceans are anywhere between 40-100 miles deep! So the basic question is--would it be tectonically feasible for Earth's oceans to be as deep as Europa's? Meaning, would it still have active plate tectonics and above-sea-level landmasses?
Europa has a surface gravity of about $13\%$ of Earth's. This means the force (weight) of the water in Europa's oceans is proportionately less than on Earth. If you divide Earth's deepest ocean depth (about $11\,km$) by $0.13$ you get a "Europa equivalent depth" of about $85\,km$, which is actually the ballpark for Europa's deepest ocean depth estimates.
Earth is much larger and because of this the gravitational pull hardly changes from the surface to a depth of only $11\,km$. Put simply water at the surface weighs about the same at the deepest point of our oceans.
This is not the same for Europa, which is much smaller. Gravity at the bottom of Europa's ocean has decreased by about $7\%$ from it's surface value, so water weighs less further down and hence has a reduced pressure. This makes it a bit easier for the internal structure of Europa to support the extra ocean depth.
There is more to this. Earth's interior structure is quite different from Europa's. Somewhere inside Europa there may be a metallic core (like Earth) but mostly it's an icy lump of water. The boundary between ocean and solid on Europa is likely to be a more like a transition between frozen and liquid states of water than the boundary between totally different materials as it is on Earth. On Earth what you see on the surface is essentially all the water their is to exist as an ocean, whereas on Europa what you have is the ocean being continuous, but freezing (or compressing) to a solid after some depth.
Could Earth support deeper oceans.
Short answer "yes", long answer "probably not a lot more".
You will hear a lot of talk about global warming melting the ice caps and increasing sea levels. So you know from this that Earth's surface can support deeper oceans, but we're not talking about a hundred kilometers more, but maybe a kilometer more at most.
As I said, Earth's gravity is far greater than Europa's and if we increased the depth of Earth's ocean by a factor of $8\times$ you would have a huge extra weight of water on Earth's surface. This would alter the balance of forces a lot and I'd be guessing but would say their their would quite a difference in the way the plate tectonics function. Landmasses above sea level seem unlikely. Earth's highest mountain ranges are limited by the ability of the material to be supported by the "sub-levels" of planet's outer layers. Adding an ocean as deep as Europa's would be like making a mountain two or three times higher - they would push into the sub-layers and sink - they'd never actually exist in the first place. An island is no different. A continent is no different either when you get down to it. So it seems unlikely we'd have much (if any) landmass about sea level.
Everest is $8\,km$ high, so adding more that $8,km$ of land (about the equivalent of $24,km$ of water) is the most weight we could expect to be supportable, but the land cannot raise that high (it's denser) so the most you can do is add about $8\,km$ of ocean depth and leave "Everest island" as practically the only land mass (with a few other tall peaks).
Plate tectonics has nothing to do with sea level; you can have plate tectonics with no water or tons of water.
Given Earth's actual landmasses, no, there would be no above-sea-level land. I am hesitant to say it is impossible on any Earth-like planet, but 40 miles seems insane to me. Mount Everest is only 5.5 miles tall. The issue is that the Earth's crust floats on the semi-liquid mantle. The higher a mountain gets, the more weight it has, and the more the crust beneath it sinks into the mantle. This causes two problems if you want really tall mountains. First, as crust under the mountain sinks, it'll drag the mountain down with it. So relative to the surrounding terrain, your mountain stops getting taller and just gets wider. It's a diminishing returns thing. One ton of rock might add a meter of height at first, but by 10km another ton might only add 20cm. Second, eventually the mountain weighs so much that the crust beneath it starts getting pushed too deeply into the mantle, and it melts. You just can't add any more material. For every ton you add to the top, a ton melts off the bottom.
But I don't think you can have 40 mile deep oceans on an Earth-like planet anyways. Water can't be a liquid below about 0.006atm of air pressure, which happens on Earth at about 12 miles. You need a much denser atmosphere, or a planet-wide sheet of ice like on Europa if you want a 40 mile deep ocean.