We extended the Broad Histogram Method in order to obtain spectral degeneracies for systems with multiparametric Hamiltonians. As examples we obtained the critical lines for the square lattice Ising model with nearest and next-nearest neighbor interactions and the antiferromagnetic Ising model in an external field. For each system, the entire critical line is obtained using data from a single computer run. We also discuss the accuracy and efficiency of our method.PACS numbers: 02.70.Lq, 05.50.+q, 75.10.HkThe search for new and more efficient methods for computer simulations is always an intensive task in science. Multispin coding techniques (see [1] and references therein), cluster algorithms [2,3,4], reweighting procedures [5,6,7] and methods which calculate directly the spectral degeneracy [8, 9, 10, 11] are a few remarkable examples (see [12,13,14] for reviews). An efficient implementation of these methods can lead to an enormous increase in speed and accuracy of computer simulations. Multiparametric simulation is another way to further improve the efficiency.Multiparametric simulations allow, from a single computer run, to explore the whole space of parameters defining a given system, instead of repeating the whole process every time some parameter is changed.