Can I purchase more storage on my apple iphone?

Note there's different kinds of "storage". Click on this link to discover what's the difference between device and iCloud storage, ways to manage your space, and upgrading to iCloud+ if you need more --> What's the difference between device storage and iCloud storage? - Apple Support

Take-away:

1. Storage on a device itself is fixed and cannot be upgraded. If you want that then you have to change your present device for one with more capacity.

2. iCloud storage is on Apple's main computers. It is not a like a normal storage hard drive but by using optimization settings on your device it can help free up device storage. Lesser used items and larger file versions can be stored in ICloud and you can get access while connected to the Internet. It does not turn a 64 GB storage device into a 64 (or whatever) + 50GB/200GB/2TB device but if you have a lot of things that aren't being used much, or you don't mind only having lesser quality photos on your device, it can free up extra space so you can make the best of the GB you do have on the device itself.

If you have upgraded iCloud storage and are seeing a message on your device that storage is full then it is possible you are not making the best use of iCloud storage and need to use optimization features. If you do have optimization activated then it is possible you are exceeding your device's needs in terms of on-device storage and you need to buy a device with more storage.

Click on the link to learn how to optimize the storage on a device --> "How to check the storage on your iPhone, iPad, and iPod touch" - How to check the storage on your iPhone and iPad - Apple Support

- "If your device is low on storage, it automatically frees up space while installing an app, updating iOS or iPadOS, downloading music, recording videos, and more.

To make more storage available, your device can remove some of your items, like streamed music and videos, files in iCloud Drive, and parts of apps that aren't needed. It also removes temporary files and clears the cache on your device. But your device only removes items that can be downloaded again or that aren't needed anymore."

Here's the same information as a video: "How to free up space on your iPhone, iPad, or iPod" - https://youtu.be/bnhuHSv_WrI

No, sorry. Storage was fixed at time of purchase. You cannot add more storage. What you can do is offload some of your data, like photos and music, to cloud storage. You get 5GB free iCloud space with your Apple ID account. You can add up to 2TB of iCloud space. See the link below for pricing.

iCloud+ plans and pricing - Apple Support

The built-in storage capacity is not upgradeable. Buy an iPhone with the storage that you will need for the duration that the phone is with you.

You can get additional iCloud storage, but that is different use than on-device storage.