Is it possible to have two moons in stable orbit of an Earth-sized terrestrial planet without apocalyptic tides, assuming the two moons together are equivalent in mass to one Luna?
@Rosella pretty well covered most of it. I'd stress two opposite constraints--to keep one moon's tide below Lunar levels, it can be bigger than Luna but then needs to orbit farther out, whereas the "Hill Sphere" is a limit on how far out it can be and still be in stable orbit around Earth. This is the radius where the gravitational force exerted by Earth's mass equals the tidal force of the Sun at that radius from Earth--tidal force rises linearly with radius, Earth's gravity falls at the inverse square, so it scales as the cube root of the ratio of mass of Earth to the Sun, and also linearly (for other planets, or imagining Earth moved to another orbital radius) with the distance of the planet from the Sun--that is the Hill sphere is actually a ratio applied to the orbital radius. At 10 AU it is ten times as great as at 1 AU. So we can't have any moon of any size at all without upper limit.
On the other hand, if you want to keep the magnitude of the tidal effect within a certain modest multiplier of the effect Luna has, it is well to remember the effect goes as the inverse cube of distance. So it is very important to consider the distance you propose each moon to orbit at. A moon of given mass has eight times the effect if it orbits at half the radius. Several moons much smaller than Luna put together can exert more severe tides on Earth than Luna, if they are a lot closer in. Meanwhile of course Earth is exerting a tide on them too, and that also rises steeply as each one orbits closer and drops if it recedes farther, again sharply. The actual acceleration as noted is a factor of the radius from the moon's center of mass, it is the rate at which that acceleration rises with that distance that varies with orbital distance measured to the center of mass.
Finally, the form of the tidal field resembles a dipole. Along the axis between the body exerting the tide's center of mass and that of the body affected, it tends to pull things away from the affected object's center of mass, but in the plane that this axis is normal to, running through the center of mass at right angles to that ray, the field actually compresses masses toward the center--at 1/2 the magnitude at a given distance. Between the ray between the centers of masses and this plane, the net field has both radial and angular components.
The upshot of this is that if we had two moons, one eight times the mass of the other but orbiting at twice the distance so its effect is identical in magnitude to the closer smaller moon, when they happen to line up (they probably do orbit in the same plane but they might not; if they do of course they line up periodically, once with both on the same side and then again with them , and even if they don't they might line up by coincidence) then their effects add, but if they are at 90 degrees to each other each one cancels out a portion (in this case identical) of the stretching effect on the main ray axis; the effect in the two perpendicular planes is more complicated, cancelling on one axis (in the plane both main rays lie in) and adding on the third axis. Thus, with these two moons, the net tidal effect is complicated. And of course both these moons' combined field is interacting with the Sun's tidal field too.
So if we have a set of moons designed to have their maximum tidal effects add up to the same magnitude as the Lunar field of OTL on Earth, in general tides will be weaker, if grouping all the moons on the same line happens rarely. Vice versa, you might get away with occasionally having tides much stronger than Luna exerts at maximum (which is roughly about twice the maximum effect the Sun ever exerts) but having them usually similar or less due to this mutual interference interaction.
And of course a habitable planet can probably handle tides considerably strong than a "spring tide" where Luna and Sol line up (happens twice a month). It means the water surges around more, and this is an influence that can contribute to overall geological heat, and can trigger earthquakes, volcanic eruptions, etc. And this represents power being dissipated and angular momentum being transferred between bodies; currently Earth's rotation is being slowed and the Moon is receding to ever higher orbit--Earth's spin angular momentum is transferred to Luna's orbital angular momentum, and some energy is transferred with it while other energy taken from Earth slowing down turns into heat. So I would guess magnitudes similar to what Earth endures currently are clearly fine but if we kick it up a factor of ten or more, that might have drastic effect on planet geology or time scales of changing spin rate, axis precession, orbital changes, etc. (This is one reason I always try to keep the magnitude similar, to avoid going into this unknown territory, also of course one wants to limit how drastic tidal effects are on the shores, how frequent and powerful earthquakes and volcanic eruptions are, etc.
Another thing about tides is that if a body is tidally locked, what matters is the rate at which material moves through changing tidal accelerations, not so much the actual magnitude of those fields. A body that is turning in phase with the field will change shape, becoming elongated on the main line of stretching force into a prolate spheroid (if it is fluid at all, but a habitable planet is probably mostly liquid outer core and plastic mantle-if we could magically turn on a powerful tide the surface would suffer badly as the planet shifts into its new equilibrium shape, but for ISOTs and so on one imagines the ASBs magically map the old planet onto the new spheroid and the crust is adjusted to the equilibrium of the fluid planet material below. Assuming this happens, liquids assume equipotential shapes so the egg shape is all one level gravitationally speaking. Of course we can imagine a formerly warm planet cooling off and freezing in a certain shape, and then the tidal effect weakening somehow, so we now have something like Larry Niven's imagined planet Jinx, with the ocean pooling around the short circumference and the Ends poking up out of the atmosphere--but if the tides that formed Jinx into that shape persisted, then the sea and air would coat the surface as though it were a sphere. (Sort of--the potential of the surface is the same, but the rate at which the potential changes as one goes upward varies depending on where one is on the egg shape, and that affects where the mass of air concentrates as lower rates of potential dropping provide more volume within a given potential range).
But the devil is in the details--I suspect it is impossible to ever have absolutely perfect tidal locking. There are perturbations acting on the system and these will tend to knock the spinning planet a bit out of whack with its orbit--in fact it is reactions from these mismatches that act to keep them largely in synch. And that means the tidal fields will not remain constant or stationary perfectly, and their fluctuations will act to move water around and so forth. So when I say for instance that you can have two Earthlike planets mutually orbiting each other with a 24 hour period, and that the massively stronger tide versus Luna's on Earth currently (they are closer to each other than Luna is to Earth, by a factor of 8 or so and thus if either were the size of Luna their tide would be 500 times stronger, but also each being Earthlike they mass 80 times more so it is 80 times 500, or 40,000 times stronger) these worlds having bearable tides depends on their staying very very closely in synch indeed; a half percent relative motion would result in tides 200 times stronger than Earth endures! Are such small relative motions, 1/200 of 1/200, adequate to keep their two spin axes lined up close enough to their shared orbital axis? I am not sure! The fact the forces get strong fast probably means they can stay in synch but perhaps it is a fact of life on any such worlds that the tidal phenomena are gigantic in magnitude, not 40,000 times what Earth experiences but maybe say 1000 times worse, or 100, or anyway 10. I don't honestly know for sure how it all works out, bearing in mind there will be strong interactions with third objects like the Sun.
