In this paper, we develop a new modified embedded atom method (MEAM) potential that includes the bond order (MEAM-BO) to describe the energetics of unsaturated hydrocarbons (double and triple carbon bonds) and also develop improved parameters for saturated hydrocarbons from those of our previous work. Such quantities like bond lengths, bond angles, and atomization energies at 0 K, dimer molecule interactions, rotational barriers, and the pressure volume-temperature relationships of dense systems of small molecules give a comparable or more accurate property relative to experimental and first-principles data than the classical reactive force fields REBO and ReaxFF. Our extension of the MEAM potential for unsaturated hydrocarbons (MEAM-BO) is a step toward developing more reliable and accurate polymer simulations with their associated structure property relationships, such as reactive multicomponent (organic/metal) systems, polymer metal interfaces, and nanocomposites. When the constants for the BO are zero, MEAM-BO reduces to the original MEAM potential. As such, this MEAM-BO potential describing the interaction of organic materials with metals within the same MEAM formalism is a significant advancement for computational materials science.