Multi-resolution grid computation is a technique used to speed up source localization with a Maximum Likelihood Estimation (MLE) algorithm. In the case where the source is located midway between grid points, the MLE algorithm may choose an incorrect location, causing following iterations of the search to close in on an area that does not contain the source. To address this issue, we propose a modification to multi-resolution MLE that expands the search area by a small percentage between two consecutive MLE iterations. At the cost of slightly more computation, this modification allows consecutive iterations to accurately locate the target over a larger portion of the field than a standard multi-resolution localization. The localization and computation performance of our approach is compared to both standard multi-resolution and single-resolution MLE algorithms. Tests are performed using seven data sets representing different scenarios of a single radiation source located within an indoor field of detectors. Results show that our method (i) significantly improves the localization accuracy in cases that caused initial grid selection errors in traditional MLE algorithms, (ii) does not have a negative impact on the localization accuracy in other cases, and (iii) requires a negligible increase in computation time relative to the increase in localization accuracy.