Optimization and control of building thermal energy storage holds great potential for unlocking demand-side flexibility, an asset that is being given much attention in current grid reforms responding to the climate crisis. As greater information regarding grid operations is becoming available, grid-interactive building controls inherently have become a multi-objective problem. Typical multi-objective optimization frameworks often introduce greater complexity and computational burden and are less favorable for achieving widespread adoption. With the overall goal of easing deployment of advanced building controls and aiding the building-to-grid integration, this work aims to evaluate the trade-offs and degrees of sub-optimality introduced by implementing single-objective controllers only. We formulate and apply a detailed single-objective, model predictive control (MPC) framework to individually optimize building thermal storage assets of two types of commercial buildings, informed by future grid scenarios, around energy, economic, environmental, and peak demand objectives. For each day, we compare the building’s performance in every category as if it had been controlled by four separate single-objective model predictive controllers. By comparing the individual controllers for each day, we reveal the level of harmony or discord that exists between these simple single-objective problems. In essence, we quantify the potential loss that would occur in three of the objectives if the optimal control problem were to optimally respond to only one of the grid signals. Results show that on most days, the carbon and energy controllers retained most of the savings in energy, cost, and carbon. Trade-offs were observed between the peak demand controller and the other objectives, and during extreme energy pricing events. These observations are further discussed in terms of their implications for the design of grid-interactive building incentive signals and utility tariffs.