Our current knowledge of Solar System dynamics is limited by a combination of unknowns, including the masses of most asteroids and the mass loss rate and oblateness of the Sun. Highly precise Interplanetary Laser Ranging (ILR) measurements have been suggested to enable the reconstruction of subtle dynamical effects, allowing the determination of several of such unknowns. Following the mission proposal by the name of Trilogy, we simulate a triple ILR setup obtaining frequent range measurements between space-based transceivers orbiting the Earth, Mars and Venus. Simultaneous spacecraft orbit determination allows for the generation of highly accurate planet-to-planet ranges by adding constant range biases as parameters to estimate at every orbit determination arc. We find that such resulting ranges can reach millimetric precision and accuracy, assuming state-of-the-art ILR hardware, accurate spacecraft dynamical modeling and favorable geometry between the ILR links and the spacecraft orbital planes. The usage of such measurements alone in a planetary batch estimation after a five-year mission is found capable of estimating the radial positions of the three planets with millimetric true errors, whereas only a few tens among the 350 main perturbing asteroids are found to get their true and formal errors reduced by a significant amount (i.e., one order of magnitude). We make a series of recommendations for future studies, including the testing of alternative mission architectures (e.g., placing one vertex around a Main Belt asteroid instead of Venus to reach more sensitivity to the asteroid perturbations) or more complex orbit estimation methods (e.g., coupled, constrained multi-arc) to get the most information out of the inter-spacecraft laser range measurements.