Is it feasible to train a single model on 150+ classes? I have classes for different regions. (Let say 80 classes for 3 regions each).
Will it be ok if I train my CNN model with 240 classes or should I create 3 models for each region? The classes for each region are similar to the classes of other region with same name but there is some difference in the elements of each class from each region and hence given some other class name.

I currently have one trained model which gives good accuracy for one region with 80 categories. Now that I have to move with remaining classes, it will be time-saving if I know beforehand to train one single model with 240 categories or three different models with 80 categories each.

I have 300 images for each class on average.
A Classifier's quality depends from the number of available observations for each class. If you have 300 images for each class, as you said above, it might be enough (it depends from the quality of your data).
In any case, it would require a massive amount of data augmentation.

Training a Network on 240 classes could be very challenging, if you don't have a proper infrastructure. That all depends on training times, but I'd suggest you to break down the problem in smaller subproblems. That would also make debugging and improvements easier to implement.