Cultural diversity and stability of a population affect the adaptiveness and survival of individuals. Besides field studies, cultural diversity and stability have been investigated with the help of different modeling approaches in relatively simple cultures. These theoretical studies helped identify mechanisms that generate cultural diversity through increasing the proportion of new elements in the population, for example by immigration or erroneous learning. Copy-the-majority learning strategies, forms of positive frequency-dependent learning, have a rather opposite effect: while they help in maintaining cultural stability by favoring the spread of common elements, they also decrease cultural diversity. We investigated whether these basic, conflicting mechanisms are sufficient together to create a complex, polymorphic cultural system and to maintain its diversity and stability. For that we developed an individual-based model simulating song learning in birds in which the extent of immigration, the frequency of learning mistakes and the strength of positive frequency-dependent learning were included as modifiable parameters. From the model, we obtained information on the composition and temporal changes in the individual and population repertoires. A comparison with long-term field data on a European passerine bird species with moderate song complexity, the collared flycatcher ( Ficedula albicollis ), was also performed. Our results confirmed that certain combinations of the three investigated mechanisms were indeed able to create patterns that showed certain aspects of polymorphic cultures. Yet, several discrepancies occurred when comparing the simulation results with the field data that emphasize the implementation of other mechanisms, especially those that have a stabilizing effect. Long-term metastable states, found in the population-level cultural diversity, raise awareness to animal cultures’ possible sensitivity to external factors.