Are the classes balanced? If you have 1000 classes but 92% of your examples are of one class, then you can get an accuracy of 92% just by always predicting the same class. What kind of error does your model makes? Have a look at the predictions (training and validation) to check that they make sense
If class imbalance is not an issue, then you might try different techniques against overfitting incl. (but not limited to): adding dropout, adding a regularisation term, decreasing the capacity of your network, etc.