What are the services for training a complex image recognition network?

Question

Pattern recognition

Good day to all!
It's no secret that there are a lot of services on the network now where you can train and configure your neural network for pattern recognition. The principle there is this: you upload a lot of pictures there (for example, cats and dogs) and manually mark up the pictures to train the service: here we have a dog, and here we have a cat. After such training, the network will be able to distinguish a dog from a cat in any image that you upload there.
So. My task is a little more difficult.
What if I give such a service a picture where there is both a cat and a dog? Or 10 cats and 15 dogs? The service will “blunt” and, at best, will detect only one animal in the picture, ignoring the rest. Those. these services are designed from the logic of 1 picture = 1 object.
I have the following task: I need to find a service that can feed 70-80 objects. He will learn from them, and in subsequent cases, when uploading a photo to it, he would find all the objects that he knows on it. And sent the coordinates for each object. It doesn't matter if there are 1 or 100 repetitions.
Are there such services?
Where to dig?