One model will work in this case.
Lets put it this way, let's say we are trying to solve multi-class(lets say 5) classification problem in neural networks we will have 5 neurons in the final dense layer and ideally use softmax as activation function and categorical_crossentrophy as loss function.
Now coming back to multi-label classification lets take an example:
Your car1 has labels like Sedan,Blue,and Type(Good).
Your car2 has labels like SUV,Black, and type(Bad).
You will these many neurons in your final layer lets say here we have 6 different types of labels for 2 cars, and we do one hot encoding for the target variables.
The difference is we use sigmoid and binary_crossentrophy as activation and loss functions. This will give probabilities of the labels for which each image belong to.
Any questions, please post.