Can i build an image classification model where each image has multiple labels?
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.