One-more problems like One-More Discrete Logarithm (OMDL) and One-More Diffie–Hellman (OMDH) have found wide use in cryptography, due to their ability to naturally model security definitions for interactive primitives like blind signatures and oblivious pseudorandom functions (OPRF). Furthermore, a generalization of OMDH called Threshold OMDH (TOMDH) has proven useful for building threshold versions of interactive protocols. However, due to their complexity it is often unclear how hard such problems actually are, leading cryptographers to analyze them in idealized models like the Generic Group Model (GGM) and Algebraic Group Model (AGM). In this work we give a complete characterization of widely used group-based one-more problems in the AGM, using the Q-DL hierarchy of assumptions defined in the work of Bauer, Fuchsbauer and Loss [BFL20]. We give two practical applications of the above results.