It is rather straightforward to add a new planet, say Jupiter. Jupiter has mass $$M_J=1.9\times 10^{27}\mathrm{kg},$$ and distance to the Sun of $5.2$ AU. The additional gravitational force the Earth feels from Jupiter in the $x$-direction is $$F_{x}^{EJ}=-\frac{GM_JM_E}{r_{EJ}^3}(x_E-x_J),$$ where $E$ stands for Earth, $J$ for Jupiter, $r_{EJ}$ is distance between Earth and Jupiter $$r_{EJ} = \sqrt{(x_E-x_J)^2+(y_E-y_J)^2},$$ and $x_E$ and $y_E$ are the $x$ and $y$ coordinates of Earth, respectively, and $x_J$ and $y_J$ are the $x$ and $y$ coordinates of Jupiter, respectively. The $x$-component of the velocity of Earth changes thus to $$\frac{dv_x^E}{dt}=-\frac{GM_{\odot}}{r^3}x_E-\frac{GM_J}{r_{EJ}^3}(x_E-x_J).$$