Generalized Maximum Entropy (GME) approach is one of the alternative estimation methods for Regression Analysis. GME approach is superior to other classical approaches in terms of parameter estimation accuracy when some or none of the assumptions of classical approaches are violated. However, determining bounds of parameter support vectors is one of the open parts of this approach when researchers have no prior information about the parameters. If support vectors cannot be determined correctly, parameters estimations will not be obtained correctly. There are some theoretical studies about GME for different datasets in the literature, but there are fewer studies about how to determine parameter support vectors. To obtain robust parameter estimations in GME, we introduced a new iterative procedure for determining parameter support vectors bounds for multilevel dataset. In this study, the new iterative procedure was applied for multi-level random intercept model and the new procedure was tested both simulation study and the real life data. The Classical and the new procedures of GME estimations were compared to Generalized Least Square Estimations in terms of Root Mean Square Error (RMSE) statistics. As a result, the estimations of the new approach provided lower RMSE values than classical methods.