Stronger than Newton's laws? According to the Newton mechanics, the force is responsible for changing the body velocity, and the body mass is the body inertia - a property to resist to the applied force. These two things make a clear sense in the Newton equation (Second Law) $ma=F$. Both "parameters" (the body mass and the force strength) are observable and measurable.
Now I am reading an article of G. 't Hooft where he states that "The interactions among particles have the effect of modifying masses and coupling strengths". So not only velocities are modified with forces but the particles masses and the forces themselves. 
I see here a contradiction with the Newton's definition of force and mass. As soon as the QFT is more fundamental than Classical Mechanics, does it mean that the 't Hooft's law is stronger than the Newton's ones? What is the impact (effect) of this stronger law on Classical Mechanics? How to define now the masses and forces if they are self-modifiable?
EDIT: OK, is there a classical physics example to demonstrate that a potential interaction can modify mass and charge?
 A: Hydrodynamics is a whole classical world when you can find most of the effects you ask about; from Archimedes change of weight to renormalisation of turbulent fluid. Were you born in the XIXth century, you would be militant against Hydrodynamics I guess :-)
If you are asking for examples without fields, with only a finite number of degrees of freedom, you are reducing the scope a lot.  But generically, the point is that you get some parameter to express departure from Newton's law. Typically, c and h. You need a finite c, besides a non zero h. Then you use many body mechanics to approach to a situation that happens to be near a finite model with small h and very big c, and this we call the classical approximation.
The idea of setting h=c=1 is computationally very practical, but a lot of people gets into problems because of it. For instance, fermionic lagrangians have really a $h$ somewhere multiplying them, so in the classical limit they dissapear; this is a reason to have classical bosonic fields only.
A: Here comes an experimentalist's view:

I accept as premise that four vectors and special relativity exist and are well documented to hold for elementary particles.
I accept that the same holds true for the Heisenberg uncertainty principle.

In special relativity mass is the "scalar length" of the four vector. When one has a specific particle, a photon, one knows the mass is 0. If one has two photons, their combined mass is not additive, it follows four vector algebra and will depend on the angles . The same will be true for two electrons, their combined mass is not additive but forms their invariant mass.
Thus the meaning of mass is different  between Newtonian physics and relativistic physics, since in Newtonian masses are additive in relativistic they are not.
Now we have the Heisenberg uncertainty principle and within a specific region $\Delta(p)\cdot\Delta(x)>h$,  momentum is not well defined nor position, thus an experiment to get at the force, $F=dp/dt$ will be indeterminate to that extent, and even for a single particle it will measure a different mass depending on the $x$ within the HP. More so when there is an interaction of two particles, and I cannot think of an experiment where a second particle will not be involved in the measurement, where the combination of the indeterminacy of momentum and the vector addition will combine to even higher uncertainty of the combined mass measurement.
This is my simple minded answer  without going into QED and virtual photons etc., where still four vector algebra will hold. There is a limit to the range in which Newtonian physics is valid. It is not possible to mix classical and relativistic and quantum mechanical  concepts of mass, so there can be no example.
A: When a mass is accelerated unruh radiation is produced. An accelerated particle moves in rindler space so boundary conditions due to the presence of an horizon causes the instability of the vacuum that produces a thermal atmosphere of particles that radiates. Also the accelerating particle produce gravitons. The very nature of inertia, and therefore mass, is veiled in mystery. The Higgs fiels is atributed with the property that it gives mass to particles. The Higgs mechanism is nothing that a well-defined mathematical procedure to give mass to Yang Mills fields while preserving renormalizability. But what is the origin of the Higgs field? Is it gravitational? Is it an artificial construction? If the Unruh radiation scenario is correct when you accelerate a mass you have to subs tract the back reaction due to the emission of gravitons and unruh rad. In response to your answer, I would say that Newtons Law is actually and approximate law of nature that cannot be used rigorously to define mass anymore. The problem is that QFT, String Theory, or M-Theory cannot be used either because there are not universally accepted. The nature of the Higgs boson is unknown, and unruh radiation or gravitons have not been detected. In this sense, the meaning of mass is still an open question.
A: The proper force on a particle is clearly defined and independent of its motion in any frame. Its rest mass can be calculated from $F = ma$ in its proper frame. There is no important contradiction to Newton's law of inertia when used this way.
A: Consider a binary pulsar with electrostatic charge 1 Coulomb in a constant electric field. As the two stars draw inwards, the potential energy of their interaction decreases their mass. So here is a modification of mass in classical mechanics.
For a modification of force, consider a charged ball falling through air, and going into pure glycerin. The dielectric constant of the glycerin modifies the force.
These examples are ubiquitous, and I don't understand the purpose of this question: Newton's laws are 300 years old, of course 'tHooft's stuff will supersede them, they have been superseded many times already.
A: I gave a popular explanation of "how our interaction modifies the fundamental constants" here and here.
