What dependencies are multiplying? I organize my code so that the very top level of the api has all external dependencies injected there, there is no public classes below a single exposed class that would need to be directly injected into. The only thing I need to actually inject are things that are outside of my memory space, ie network calls, event buses, dbs. If it's not using something outside of my memory space I am just using new inside my classes, it's far easier to test.
For example, if I'm adding a new feature to allow a user to change their address, I would have a single class at the top level "CustomerAddressChange" or whatever. I would inject an interface that wraps everything external, and that is the only thing that anything would be injected into. My tests would all stub only that interface. Everything else is done without any sort of DI container.