If your application is capable of pushing data in multiple streams but you are still facing issues. Then you may want to check if network is a bottleneck between client and server.
Its good idea to start with single stream and verify how much data can be pushed. Increase number of streams linearly until performance is increasing linearly. So we know at what level we start getting constant output e.g you should see linear increase in throughput as we increase the number of stream. At one point you may see the same throughput Or very small change in result. And that’s the time you should start looking into other aspects to see if there is any other bottleneck.
Most of the S3 compatible applications give option to tune data upload to S3 endpoint. One of the important configuration option is to choose between a single stream vs multiple streams for uploading data.