We propose a simple microfluidic approach: Dissolution-After-Precipitation (DAP), to investigate regimes of carbonate rock dissolution and multiphase reactive transport. In this method, a carbonate porous medium is created in a glass microchannel via calcium carbonate precipitation, after which an acid is injected into the channel to dissolve the precipitated porous medium. Utilizing the DAP method, for the first time we realized all five classical single-phase carbonate rock dissolution regimes (uniform, compact, conical, wormhole, ramified wormholes) in a microfluidic chip. The results are validated against the established theoretical dissolution diagram, which shows good agreement. Detailed analysis of these single-phase dissolutions suggests that the heterogeneity of the porous medium may significantly impact how the dissolution patterns evolve over time. Furthermore, DAP is utilized to investigate multiphase dissolution. As examples we tested the cases of an oleic phase (tetradecane) and a gaseous phase (CO₂). Results show that the presence of a nonaqueous phase in pore spaces induces the formation of wormholes despite weak advection, and these wormholes ultimately become pathways for nonaqueous phase transport. However, the transport of tetradecane in the wormhole is very slow, causing acid breakthrough into neighboring regions. This mechanism enhances lateral connectivity between wormholes and may lead to a wormhole network. In contrast, CO₂ moves rapidly and continuously seeks to enter a widening wormhole from a narrower wormhole or the porous regions, generating phenomena such as ganglia redistribution and counterflow (flow of gas opposite to acid flow). Extensive independent experiments are conducted to verify the reproducibility of the observed phenomena/mechanisms and further analyze them. Real-time monitoring of fluid pressure drop during dissolution is implemented to complement microscopy image analysis. Our method can be implemented repeatedly on the same chip, which offers a convenient and inexpensive option to study pore-scale reactive transport mechanisms.