Little is known about the evolution of continental ice sheets through the last two glacial inceptions. Here, we present a relatively large perturbed parameter ensemble of transient simulations of the last two glacial inceptions and subsequent interstadials (Marine isotope stages, MIS 7e-6e, 240-180 ka and MIS 5e-4, 120-60 ka) with the fully coupled ice/climate model LCice. LCice includes all the critical feedbacks between climate and ice. As shown herein, it can capture the inferred sea level change of the last two glacial inceptions within proxy uncertainty. One key underlying question of paleoclimate dynamics is the non-linear state dependence of the climate system. Concretely, in a model-centric context, to what extent does the capture of one climate interval in an earth systems model guarantee capture of another interval? For LCice, the capture of present-day climate is insufficient to predict capture of glacial inception climate. Furthermore, the capture of inferred sea level change in one inception has weak correlation with the same outcome for the other. After partial history matching against present-day and past sea level constraints, the resultant NROY (not ruled out yet) ensemble of simulations have a number of features of potential interest to various paleo communities, including the following. (i) In correspondence with the inferred last glacial maximum configuration, the simulated North American ice sheets are substantially larger than the Eurasian ice sheet throughout MIS 5d-MIS 4 and MIS 7d-MIS 6e. (ii) Hudson Bay can transition from an ice-free state to full ice cover (grounded ice) within 1000 years. (iii) North American ice sheets expanded on average at 170 +- 40 m/yr at southern margin during both inceptions, while the Eurasian ice sheet grew 50 +- 70 m/yr from MIS 5d-c and 100 +- 70 m/yr from MIS 7d-c. (iv) the Laurentide and Cordilleran ice sheets merge in their northern sectors in all NROY simulations for MIS 7d, contrary to what is assumed from limited geological data. (v) larger ice sheets display a larger lag in the timing of stadial maximum ice volume compared insolation minimum; the North American ice sheet maximum lags 3.7-4.5 kyrs behind the MIS 7d insolation minimum. Supplemental resources include a dynamic display of ice advance and subsequent retreat for a sub-ensemble of 15 simulations from MIS 5d-4 and MIS 7d-6e.