Identifying and mitigating small-signal instabilities in the modern converter-based power system consisting primarily of grid-following (GFL) and grid-forming (GFM) converters is a significant challenge for transmission system operators (TSOs). This is primarily due to restrictions imposed by intellectual property rights (IPRs) on original equipment manufacturers’ (OEMs) models for generating units and other grid-connected equipment. Consequently, TSOs rely on black-box models, which are encrypted models limiting access to their inputs and outputs, severely limiting the TSOs’ ability to identify the root-cause for small-signal instabilities. Ideally, the risk of these instabilities occurring should be limited during the grid-connection process before grid integration. However, due to the IPRs this becomes inherently impossible as the TSOs are unable to gain insight into the internal dynamics of the models, impeding the TSOs in ensuring the stability and reliability of the power system. Generally, GFL converters typically perform well in stiff grids but may introduce small-signal instabilities under weak grid conditions, whereas the opposite applies for GFM converters. However, the complex interactions among multiple converter-based resources under varying operating scenarios (OSs) further complicate stability prediction, highlighting TSOs' need for deeper insights into converter interactions before grid integration. Hence, to tackle this challenge, this paper proposes a structured, collaborative study framework between TSOs and OEMs. This framework includes OEM-provided black-box state-space models enabling the TSOs to execute an automated analysis process comprising load-flow and eigenvalue-based stability analysis for screening representative OSs which may result in instability. Finally, a participation factor analysis for root-cause identification will determine the contribution from the system states to the identified instability. Upon identifying the root-cause of the instability, the OEMs can perform the relevant modifications, such as control tuning or in collaboration with the TSO perform other mitigation actions. The effectiveness of the proposed study framework is demonstrated through a practical case study involving the grid-connection of a wind power plant using GFL controls into a converter-based power system. During weak grid conditions, interactions between converters and the power system led to small-signal instability, which was systematically identified and resolved using the proposed study framework resulting in a stable and reliable grid. Electromagnetic transient simulations are given to verify the theoretical analysis of the proposed study framework.