This is not as simple a question as it looks.
One has to decide what it means to "test an equation", and usually this means that an alternate form of the equation is posited with some extra parameter(s), such that if this parameter is zero the original equation is recovered. For example, Newton's 2nd law could be expressed as F = ma + x, and experiments undertaken to measure x.
However, there are an infinite number of such forms. For example, I could also write down F = (1 + y)(ma), and try and measure y.
Where it gets complicated is when you have multiple equations. For example, I can posit a modified Faraday's law:
\nabla \times \mathbf{E} = -(1+k_1) \frac{\partial \mathbf{B}} {\partial t}
and I will discover there are very stringent limits on k1: it's smaller than 10-10.
Likewise, I can instead modify Ampere's Law to get
\nabla \times \mathbf{B} = \mu_0\mathbf{J} + (1 + k_2) \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}} {\partial t}
and I will again discover there are very stringent limits on k2: it's also smaller than 10-10.
However, if I made both changes, what I will discover is that | k_1 + k_2 | < 10^{-10}, but my actual constraints on k1 and k2 individually are about a thousand times weaker. So by going from a theory with one extra parameter to one with two, I can evade many experimental limits.
Put another way, I can always find a (arbitrarily large) set of parameters that will agree with measurements. But that's not very useful. What is more useful is a model with a small number of additional free parameters. One of the most well known is the Proca theory, which has:
\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0} - \mu^2 \phi [/itex]<br />
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and <br />
<br />
\nabla \times \mathbf{B} = \mu_0\mathbf{J} +\mu_0 \varepsilon_0 \frac{\partial \mathbf{E}} {\partial t} - \mu^2 \mathbf{A}<br />
<br />
where \phi and \mathbf{A} are the potentials of the electric and magnetic fields, and \mu is a new parameter of the theory. It has dimensions*, which is maybe not so nice (a pure number would be easier to interpret), but experimentally it is very small: about 10<sup>-30</sup> meters.* It has to, because it links fields and potentials, which have different dimensions.
