<p>I can't give you a number, but a method to find it yourself. The technique is plotting a graph called "<strong>learning curve</strong>" where the x-axis is the number if training samples and the y-axis is the score. You start at 1 training sample and increase to 600. You plot two curves: the training error and the test error. You can then see how much influence more data without any other change will have on the result.</p>

<p>More details and the following image in <a href="https://arxiv.org/pdf/1707.09725.pdf" rel="nofollow noreferrer">my masters thesis, section 2.5.4</a>:</p>

<p><a href="https://i.stack.imgur.com/Jxj6T.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Jxj6T.png" alt="enter image description here"></a></p>

<p>In this example you can see that having up to 20 training samples each new example is improving the test score a lot (green curve goes down a lot). But after that, throwing just more data at the problem will not help a lot.</p>

<p>The curve will look different in your case, but the principle should be the same.</p>

<h2>Other analysis</h2>

<p>Look at chapter 2.5 and 2.6 of my masters thesis. I especially recommend having a look at the confusion matrix and <a href="https://datascience.stackexchange.com/a/25008/8820">confusion matrix ordering</a>. This will give you an idea which classes are confused. Maybe the classes are just inherently difficult to distinguish? Maybe one can add more features? Maybe there are labeling errors? Have a look at chapter 2.5 for more of those "maybe's"</p>
Specific amount of training data required for fine-tuning Resnet-50 model
<p>for decent generalization, how many images per class is needed for fine-tuning the Resnet-50 model for ASL HandSign Classification(24 classes)? I have around 600 images per class and the model is overfitting very badly.</p>