We develop a framework of construction strategies for traceability codes on the subject of multimedia fingerprinting, which constructs traceability codes in a concatenated way. In fingerprinting systems, there are tradeoffs among the size of the customer base, the collusion resilience, and the codeword length. Our goal is to find a strategy to construct, traceability codes that reach an equilibrium among these tradeoffs. Instead of investigating a "high-performance" code, which has proven challenging in existing researches, we introduce a concatenated construction methodology to provide a flexible approach for producing more applicable traceability codes by composing several existing "low-performance" collusion-secure codes. Instead of just giving an example constructed by specific codes, we describe a general code construction strategy and give a detailed analysis on it. Moreover, we propose two concatenated construction schemes based on group fingerprinting to show the feasibility of the concatenated construction strategy. Experimental results show good performances on the code length, detection time, and tracing ability.