That’s a great question. To figure this out, I’d like to ask you a few questions about what you are trying to achieve exactly and your store.
I understand your intention is for the eligible customers to pick which option is best for them at check out, is that correct? What are the conditions for the customers to be eligible? Are you using the Shopify app Local Delivery to set up this feature? If so, are you able to set up both options in the admin, but then afterwards don’t see them at checkout?
It would be very helpful to see what are the steps you are following to try and set this up. Can you send a screenshot of the setup or reply with the detailed steps?
Thank you for replying with the screenshots. I’ve had a look at this for you, and it seems that at this time, when a customer is eligible for multiple rates, the page will always offer the cheapest one as seen here. This means that you can add multiple locations and different rates depending on the value of the cart, but the system will always apply only one, be either the cheapest or the corresponding one depending on location or cart value.
There might be advanced shipping apps in our store, however, that can help you set up more complex shipping options.
On the other hand, as you also want to have a third party option, I would like to ask you if you have set up this service. Is it showing at checkout as a second shipping option, or you are only seeing the Local Deliver? If you like, you can share your store url and test shipping address, so we can take a look at your checkout.