In my case (as a long time customer), I rang UPC/Sunrise and asked them that exact question - plus, would I have to swap the modem and lose internet for a day or two.
They simply reduced my monthly price to match the Sunrise one, so I kept everything but got the new price. It’s worth a try.
I do get two separate bills now, though - one from Sunrise for my mobile and one from UPC for my TV and internet.