Open Radio Access Networks (Open-RAN) trigger a shift from conventional monolithic RAN architectures to disaggregated designs with open interfaces, diversifying the 5G supply chain and boosting innovation. It is envisaged that Open-RAN deployments will be heavily software-based, allowing for higher flexibility and faster integration of new features. However, existing software-based solutions, seem to be unable to realize practical and standard-compliant Multiple-Input, Multiple-Output (MIMO) designs with a large number of concurrently transmitted information streams, as the 5G New Radio standard requires in order to substantially improve connectivity and throughput. In this context, we introduce MIMO-SoftiPHY, the first 3GPP and Open-RAN compliant, software-based physical layer (PHY) design and implementation framework that can practically realize MIMO designs with large numbers of information streams in a power-efficient manner. MIMO-SoftiPHY is inherently integrated with OpenAirInterface, enabling practical, software-based MIMO deployments with commercial-off-the-shelf user equipment. Specifically, MIMO-SoftiPHY achieves real-time performance for 12 MU-MIMO streams at a 10MHz bandwidth and 8 streams at a 20MHz. In addition, and in contrast to existing designs, MIMO-SoftiPHY can also support non-linear base-station processing in real-time that, as we show, can result in substantial power savings at the radio side, by obviating the need for a " massive " number of base-station antennas.