Hi,
There is no such mechanism in browsers.
Just look at Gmail. If you have an account there and you receive an email with several attachments, it will allow you to download each one with its own link and you'll also have a link to download all of them at once. That link will actually run a process on Gmail's servers to zip the attachments into one file and then send to the browser that one zip file.
And if they didn't do what you're talking about in Gmail, and since I also don't know of any such existing capability in browsers, I don't think you'll be able to do what you want.
If the files are big, I recommend you leave it like it is by default as I don't think you'll be able to improve the situation.