Yes there is. The most basic of which is kaluza-klein theory. To quote the tag wiki I wrote:

kaluza-klein theory is a classical theory that unifies gravity (general-relativity) and electromagnetism (maxwell-equations). Kaluza - Klein theory shows that general-relativity in 5 dimensions is equivalent to general-relatvity plus maxwell-equations in 4-dimensions.

supergravity is an extension of kaluza-klein which also unifies the weak force and the strong force, and with supersymmetry.

See also this answer of mine. Summarising the main points of that answer,

**Classical** General Relativity and **Classical** Electromagnetism are unified in Kaluza-Klein-Theory, which proves that 5-dimensional general relativity is equivalent to 4-dimensional general relativity plus 4-dimensional maxwell equations.

Obviously, this already agrees with your premise, since Maxwell's theory unifies Electricity and Magnetism, and now, there is additionally the gravitational force.

This is really intuitive and interesting, in my opinion.

A byproduct, though, is the scalar field known as a "Radion" or "Dilaton" which appears due to the "55" component of the metric tensor. In other words, the Kaluza-Klein metric tensor equals the GR metric tensor with maxwellian components on the right and the base; but then obviously, you have an extra field down there.

$${g_{\mu \nu }} = \left[ {\begin{array}{*{20}{c}} {{g_{11}}}&{{g_{12}}}&{{g_{13}}}&{{g_{14}}}&{{g_{15}}} \\ {{g_{21}}}&{{g_{22}}}&{{g_{23}}}&{{g_{24}}}&{{g_{25}}} \\ {{g_{31}}}&{{g_{32}}}&{{g_{33}}}&{{g_{34}}}&{{g_{35}}} \\ {{g_{41}}}&{{g_{42}}}&{{g_{43}}}&{{g_{44}}}&{{g_{45}}} \\ {{g_{51}}}&{{g_{52}}}&{{g_{53}}}&{{g_{54}}}&{{g_{55}}} \end{array}} \right]$$

Imagine 2 imaginary lines now.

$${g_{\mu \nu }} = \left[ {\begin{array}{*{20}{cccc|c}} {{g_{11}}}&{{g_{12}}}&{{g_{13}}}&{{g_{14}}} & {{g_{15}}} \\ {{g_{21}}}&{{g_{22}}}&{{g_{23}}}&{{g_{24}}} & {{g_{25}}} \\ {{g_{31}}}&{{g_{32}}}&{{g_{33}}}&{{g_{34}}} & {{g_{35}}} \\ {{g_{41}}}&{{g_{42}}}&{{g_{43}}}&{{g_{44}}} & {{g_{45}}} \\ \hline {{g_{51}}}&{{g_{52}}}&{{g_{53}}}&{{g_{54}}} & {{g_{55}}} \end{array}} \right]$$

So the stuff on the top-left is the ordinary 4-dimensional metric tensor you know from 4-dimensional GR, and the stuff on the edge ($g_{j5}$ and $g_{5j}$) is for electromagnetism (and magically comes from 4+1=5-dimensional general relativity).

... And you have an additional component on the bottom right (which you can still derive a field equation for). This is the radion/dilaton.

However, just as an addition, what about the weak and strong interactions? Surely, they exist, too! . Luckily, we have an extension to kaluza - klein called supergravity, which additionally

talks about the weak and strong forces, and requires supersymmetry.

... Which we know, lies in the low - energy limit of string theories.

Related: http://physics.stackexchange.com/a/76370/23119