Multiple upload but upload files separately to not overload PHP

I'm currently working on a photoalbum thing on my website and was wondering is there is a way to upload files separately even though I selected multiple files for upload, let me explain:

<form method="post" action="upload.php" enctype="multipart/form-data">
    <input name='uploads[]' type="file" accept="image/*" multiple>
    <input type="submit" value="Send">
</form>

<?php
$y=count($_FILES['uploads']);
for($x=0;$x<$y;$x++) {
    echo $_FILES['uploads']['name'][$x];
    echo "<br>";  
}
?>

So I've got these simple lines of code. And basically (As you can see) you can upload multiple files. But let's say that that my 'upload_max_filesize' is at 8M. I can only select 4 images of 2MB each to upload successfully, otherwise I overwrite the max upload size. My question is, is there a PHP way to keep the form structure the same but let the script handle one file at the time so I can upload 5.000 files from 5MB's each for example?