While Newtons 2nd law cannot predict the constancy or upper limit of speed of light, c, its generalized version i.e.changing mass with constant acceleration definition can do. In other words, Newtons law holds when an active force applies on a object and cannot accelerated it as long as there is an active change in mass (experimental verified). This explains the constancy of speed of light without need for Lorentzian/special relativistic mechanics.
The podtulate of constancy itself is another issue.. It is reasonable since light is the fastest process and infinite speed makes no sense, mathematically and causally. Still, some consider it an assertion
Yes it is possible if you consider space is full with energy and having negative pressure. The energy is of vacuum and so have a friction coefficient, this friction coefficient is considered as an universal constant and so the inertia of the object increases with time when it is accelerated & gain energy. The limit of the acceleration of the object will be zero after a long time and so there is a limit speed for every corpuscle declared as universal constant so Lorentz transformations...etc, so migration to Special Relativity. Friction of the space is compensate by the negative pressure of space so there is no friction at all and we still in the Newtonian model of space. This is the limit between General Relativity and classical mechanics: vacuum have energy in negative pressure.
The problem isn't the inertial mass-that is invariant under Lorentz transformations, it's that 3-vectors (the acceleration and the force) aren't invariant under Lorentz transformations. How to write the equation of motion for a relativistic particle, however, is known.
That the speed of light is invariant under Lorentz transformations is a special case of the property that any wave equation is invariant under Lorentz transformations. Maxwell's equations imply that the fields satisfy wave equations.
In this case equation of motion should be related to General Relativity in its approximation when the curvature of space time is considered flat: the garvitational field of the mass will containt constant lambda and c. Of course there is vacuum energy (function of universal constants only) and negative pressure. However we can calculate the components of the 4-acceleration and see which can complie with Newton mechanics.
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