The semantic relation between a verb and an argument can be marked by a case markers such as affixes, clitics or adpositions. A case marker can express more than one case meaning. The adpositions preceding source arguments in Chinese dialects can have other semantic roles such as path, instrument, reason, agent, etc. This paper tries to explain how the case meaning ‘source’ can be expanded to other case meanings, to establish conceptual space of a group of case meanings which are related directly or indirectly to the source meaning and to draw the semantic maps of source-related cases in many Chinese dialects. Expansion of the case meaning is caused by two crucial cognitive inferences, metonymy and metaphor. Metonymy can explain how the two routes of case expansion, ‘source-path/location-goal’ representing a motion tier and ‘agent-instrument-theme’ a action tier, are formed. Metaphor can explain how the three case meanings, source, path and goal on motion tier are mapped to agent, instrument and theme on action tier respectively.