Our current installation does not allow us to resize images after uploading them to the blog. This makes it difficult to control the size images. Images like diagrams and graphs can be hard to read if we cannot resize them to something larger.
Something like this plug in my solve the issue: https://wordpress.org/plugins/resize-image-after-upload/
@srodlund, that plugin allows you to set a maximum width and height for uploaded images along with a few other feature flags and then it checks and possibly modifies images as they are uploaded. So basically it only does things that can be done locally to an image before uploading.
Is that the feature set that you are looking to add, or did you really want to do something else? I'm wondering if what you are really looking for is some customization of add_image_size settings to either adjust the thumbnail, medium, and large sizes or to add entirely new sizes? The "if we cannot resize them to something larger" part of your task description makes me think that this is about display sizes and not raw media.