One little-known tip is to call your provider - I use both VZW and ATTWS - is to call CS but not from your mobile and ask for a Level 1 or 2 Tech and ask them to re-provision your line (or account if you have multiple lines on the network. They'll push settings to your phone, instruct you to power down the iPhone and wait, then tell you to power it back up. You may need this re-provisioning a couple of times, but they'll be able to tell you that you're properly registered on their network. This isn't the same as "resetting network settings".
I've got around 50 employees working for me, often in rural areas. A re-provisioning for them when they're in an area for a few days for field work gets them from a "fringe" connection to a solid one. Again, call from a phone other than your handset to be provisioned as you'll stay on the line with the tech while they're working on it...
I had issues with iOS 10 with my 6S+ - 9.3.5 was hugely better for retaining a connection for both ATTWS and VZW, and only the latest Beta FW seems to improve both the cellular and BT radios. Maddeningly for me is that my iPad Air 2 is the only VZW device that gets a rock solid connection with zippy data speeds. iOS 10 tanked my iPad Pro and my iPhones - I'm on the road a lot, and tether to my iPads (good old legacy UL data!!!). My weBoost eqo just showed up and I'll be setting it up in a bit. Happy Holidays!