This article optimizes the allocation of external current demand among parallel strings of cells in a lithium-ion battery pack to improve Fisher identifiability for these strings. The article is motivated by the fact that better battery parameter identifiability can enable the more accurate detection of unhealthy outlier cells. This is critical for pack diagnostics. The literature shows that it is possible to optimize the cycling of a single battery cell for identifiability, thereby improving the speed and accuracy with which its health-related parameters can be estimated. However, the applicability of this idea to online pack management is limited by the fact that overall pack current is typically dictated by the user, and difficult to optimize. We circumvent this challenge by optimizing the internal allocation of total pack current for identifiability. We perform this optimization for two pack designs: one that exploits switching control to allocate current passively among parallel strings of cells, and one that incorporates bi-directional DC-DC conversion for active charge shuttling among the strings. A novel evolutionary algorithm optimizes identifiability for each pack design, and a local outlier probability algorithm is then used for diagnostics. Simulation studies show significant improvements in diagnostic accuracy for an automotive protocol.