Time-frequency representation (TFR) is of great significance for capturing and analyzing nonlinear or nonstationary multi-component signals. The adaptive linear chirplet transform (ALCT) has proven effective for dealing with signals with frequencies that intersect, providing accurate estimations of instantaneous frequencies (IFs) for both intersecting and non-intersecting components. However, challenges still exist when handling signal components that have overlapping amplitudes, and when performing reconstruction, the components are mixed around the time of the intersection. To overcome these issues, we present the enhanced ALCT (EALCT) approach that synergistically combines several methods to overcome the previously described issues with the ALCT algorithm. The EALCT identifies the IFs by a modified ACLT as a set and separates them using the ridge path regrouping (RPRG) algorithm. Subsequently, the IFs and the corresponding chirp-rates of each component are employed to reconstruct the signal using an algorithm based on the chirplet transform. By implementing this approach, the EALCT accurately reconstructs the components with intersecting amplitudes at the time of intersection as well as the original signal. The EALCT also maintains the performance of the ALCT when applied to signals that do not have components with intersecting amplitudes, such that the proposed approach does not detract from existing success. The power of the EALCT is demonstrated using analytical and experimentally measured nonlinear and nonstationary signals and the results are compared with those produced by the ALCT.