The use of Agile in the software development industry in the past two decades revealed that it is lackluster in some aspects, such as in guaranteeing user involvement and assuring that the right software is being built. There are reports that combining Agile with Lean Startup and User-Centered Design (UCD) helps in overcoming these shortcomings while also yielding several other benefits. However, there is not much documentation on how to use this "combined approach" and adapting existing organizations to use it is a challenge in of itself, in which the use of an instrument to guide or assess such transformations is typically pivotal to their success. As such, in this paper we seek to identify maturity models that assess the use of Agile, Lean Startup, and UCD. We conducted a systematic literature review of maturity models for these three methods published between 2001 and 2020. We characterized the maturity models and determined how they see maturity, how they are applied, and how they were evaluated. As an extended version of a previous paper, we augmented our analysis criteria and further classified the models in how they interpret maturity and what strategy they suggest when undergoing an improvement process, in addition to providing new insight on various aspects of the models. We found 35 maturity models, of which 23 were for Agile, 5 for Lean thinking, 5 for UCD, and 2 for Agile and UCD combined. No models for the combination of the three methods were found (nor for Lean Startup), as expected due to the novelty of the approach. Existing models mostly focus on practice adoption and acquiring continuous improvement capabilities, and are typically developed with a specific context in mind. We also note a lack of proper evaluation procedures being conducted on the majority of models, which could be due to the lack of well-established maturity model development methods and guidelines.