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The study investigates how different constellations of agile and plan-driven project management methods used by in- and out-suppliers, out-supplier reputation, and satisfaction with the in-supplier affect intentions to choose the out-supplier for a new professional service, and whether these effects are mediated by perceived switching costs. This is a survey-based study with 971 participants in Switzerland using scenarios about a new digital business solution. The data were analyzed using path analysis and analysis of variance. The intention to choose the out-supplier is highest when the out-supplier uses agile methods while the in-supplier uses plan-driven methods. Higher out-supplier reputation leads to lower perceived switching costs and higher intentions to choose the out-supplier. Higher satisfaction with the in-supplier leads to higher perceived switching costs and lower intentions to choose the out-supplier. The results extend previous research by showing that the constellation of project management methods has stronger effects on perceived switching costs and intentions to choose the out-supplier than have out-supplier reputation and satisfaction with the in-supplier. While perceived switching costs depend more strongly on out-supplier reputation, intentions to choose the out-supplier depend more strongly on satisfaction with the in-supplier. Out-suppliers can increase their acquisition rate by using agile methods when competing with an in-supplier using a plan-driven approach. Out-suppliers should proactively communicate the benefits of agile approaches in the business initiation stage, invest in proactive reputation management, and carefully analyze the existing business relationship between the target customer and the in-supplier. If the target customer is satisfied with the in-supplier using an agile approach, it is less likely that the out-supplier will successfully outcompete them. This study is the first to examine the effects of different constellations of project management methods in addition to out-supplier reputation and satisfaction with the in-supplier on perceived procedural switching costs and the intention to choose the out-supplier. [ABSTRACT FROM AUTHOR]