Q: Is there any way to increase storage internal or external on an iPhone?

Not possible.

If you need to free up storage space, help here >  http://www.huffingtonpost.com/2015/01/08/iphone-free-space-tips_n_6269756.html

There is no way to increase the internet storage of an iPhone.

I don't know of any way to increase the external storage.

SanDisk (among others presumably) make a memory stick for the iPhone. I've no idea how it works in terms of transferring files to / from it but maybe look into that. You could also use the cloud (dropbox / google drive, etc.) though it may be slightly impractical.