The TARGET-APPROXIMATION-MODEL (TAM) is a syllable-based model to represent articulatory trajectories and pitch contours by a compact set of target parameters. In this work, we extended the TAM by an additional degree of freedom, namely the position of the target boundaries. This feature was integrated in the open-source software TARGETOPTIMIZER (TO), which is now officially updated to version 2.0 (TO2). The TO2 transfers articulatory trajectories into TAM parameters using a joint optimization with regularization. We demonstrate that the boundary optimization significantly reduces the modelling error compared to the case without boundary optimization. As an additional feature, the TO2 allows to initialize the boundaries uniformly across an utterance. Therefore, a prior determination of the syllable boundaries is no longer a necessary requirement in order to find the optimal targets. The TO2 is written in C++ and available for download as an open-source software under the GNU General Public License.