Quite easily. Imagine 2 bodies of equal mass moving at a constant speed on opposite sides of the same circle centered on a fixed point under the influence of a mutual attraction. They are experiencing equal and opposite forces, while the total momentum (and mass moment) of the 2-body system is 0.
Under a Lorentz transform, say, along the y-axis, where the circle is in the xy-plane, to a frame in which the 2-body system is moving steadily upward along the y-axis, there is a transform of synchronization in the y-direction as well, such that the body higher on the y-axis has a later clock reading than the one below it. So, it crosses the y-axis first, as it rounds the corner.
That means the two bodies are not experiencing equal and opposite accelerations. And it means the total of the forces they are subject to are not equal and opposite; nor is the total mass moment, relative to the position of the moving center. There's a deficit brought about by the desynchronization of the two bodies; a little bit of the "equal and opposite" action-at-a-distance force of the upper body on the lower one hasn't yet reached the lower body but is lingering somewhere between the two.
Recall: the action at a distance in Newton's Third Law says "equal and opposite forces AT THE SAME TIME" (i.e. propagating at infinite speed) "between the two bodies [in a direction parallel to the line separating the bodies]" The Lorentz transform of instantaneous action or infinite speed is finite speed faster than light. So, for Newton's Third Law to be consistently translated to relativistic form, you would need to somehow account for this in-between condition of the extra impulse that has not yet gotten to the other body.
The usual No-Interaction theorems (Leutwyler, Haag) assume that many-body dynamics have additive momentum - that is: that the momentum of the system is equal to the sum of the momenta of its parts. As a result -- almost directly, as you see by the description above -- it concludes that the interaction between the bodies must be 0. The way the Leutwyler Theorem is proven is to start out by assuming that angular momentum and momentum are additive, that energy is additive, up to the inclusion of many-body potential, and that the total mass momentum transforms consistently under Lorentz transforms. It stumbles into the above-mentioned problem with the mass moment deficit (because it had already started out by by assuming the momentum deficit was 0) and draws from this the conclusion that the potential energy must also be 0.
In non-relativistic theory, it is actually possible to codify the instantaneous transmission of impulse as a symplectic representation of the Galilei group (or equivalently: a mass 0 representation of the Bargmann group); whose principal features are (a) that they have an invariant momentum-squared, which might be regarded as the value of the impulse associated with the representation, (b) are instantaneous (no time translation invariance) and (c) no mass. So, a continuously-acting force might be regarded as a time-densitized continuum of such representations.
Perhaps a similar thing might be possible in relativity. The relativistic versions of the symplectic representations just described above are both the luxon (light speed) and tachyon (faster than light speed). The former might be regarded as a carrier of the radiation, the 1/r part of a force. In contrast, the latter might be regarded as a carrier of instantaneous 1/r^2 part of a force. In electromagnetism it is marginally possible to completely account for electromagnetic forces as a transmission of luxons. But ultimately it led to the Wheeler-Feynman absorber theory, whose problems were never fully resolved.
The idea of using the latter possibility was probably considered first by Wigner when he laid out the "Wigner classification" in 1939 (out of which we get the classes: bradyon/luxon/tachyon/homogeneous). He said in the 1939 paper that he eventually wanted to get back to the tachyons, but apparently never got around to it ... until much later.
A lot of people tried to devise different formulations for a consistent relativistic many-body dynamics in the 1950's-1970's; and probably the best push in that direction was the general framework that Van Dam and Wigner laid out for possible action-at-a-distance forces mediated by faster-than-light non-instantaneous lines of force. ("Classical Interacting Relativistic Mechanics of Interacting Point Particles", Physical Review, 138, B1576-1582, 1965; "Instantaneous and Asymptotic Conservation Laws for Classical Relativistic Mechanics of Interacting Point Particles", Physical Review, 142, 838-843, 1966.)
Apparently, that was Wigner's "finally getting back to the tachyon" issue, though he didn't specifically state it as such. Nonetheless, his and Van Dam's description amounts to doing the very kind of time-densitized smearing out of representations that I described above. (The integrals used to describe the interaction, in fact, express a time-smeared continuum of luxons and/or tachyons between the interacting bodies; they consider both sets of possibilities.)
In the view espoused in Van Dam and Wigner's treatments, these representations are not "particles" but merely the relativistic version of Newton's instantaneous lines of force caught in an in-between state. They account for the momentum deficit in a way that is compatible with the Lorentz transformation.
There's one more recent approach that I've seen that carries promise in that direction, though the author does not explicitly sell it as a "force mediated by FTL action-at-a-distance" idea. (Actually he sorta does: below equation (23) in his paper where it says q is a "spacelike momentum" -- well, that's just another name for a tachyon. He acknowledged that point, but still insisted on shying away from it.)
Reverse Engineering Approach to Quantum Electrodynamics
Smilga
arXiv: 1004.0820v2 physics.gen-ph
In his approach, when one lays out the 2-body scattering scenario used in the perturbative S-matrix formulation of quantum field theory, the initial "in" state consists of 2 bodies, as does the final "out" state; but the intermediate states are also given interpretation as consisting of a 2-body system, that has a well-defined total momentum (P = p0 + p1) but is an entangled state with an intermediary (q) that effectively communicates that entanglement.
The out state that emerges can be thought of as doing a momentum measurement on one of the two bodies (p0') which clamps down on (q), and which by virtue of the relation (p1' = P - p0') also clamps down on the momentum of the other body. Whatever the difference is I = p0' - p0, is an impulse in effect that is equal and opposite to the impulse -I = p1' - p1 of the other body. So, a separated in state becomes an entangled interacting state, and separates again as an out state after the impulse is transmitted via the entanglement.
He actually goes on, and develops that idea further (in other articles) that action at a distance can, itself, be constructed in a similar way via entanglement; though I think he goes too far in trying to do such things as derive the fine structure constant from all this!