Fluorite-structure ferroelectric field-effect transistors (FeFETs) are among the most promising candidates for in-memory computing (IMC) owing to the complementary metal-oxide semiconductor (CMOS) compatible process, high scalability with decent remanent polarization, and ultra-fast response. However, for on-chip training, a major obstacle in implementing FeFETs is the limited endurance. Here, we demonstrate a run-time reconfigurable (RTR) device that enables mode switching between an unlimited-endurance dynamic random-access memory (DRAM) mode for on-chip training and a non-volatile FeFET mode for inference. Even more excitingly, the RTR device features a monolithically 3D stacked two-transistor structure, utilizing an oxide-semiconductor channel and Zr-doped HfO2 (HZO) ferroelectric with back-end-of-line and CMOS compatibilities. In addition to DRAM and FeFET modes, logic mode is also realized in the RTR device. Furthermore, a hybrid IMC system using RTR devices is proposed, achieving a high image classification accuracy of 91.6% with long-term retention and without endurance loss during 8-bit quantization training. Our work of 3D stacked multiple functional devices can be a game changer that unlocks new possibilities in device architecture for future data-intensive computing.