This isn't so much an android tv question as it is a networking question.

Good place to start would be posting what equipment you have (modem and router), what devices you are streaming to, and what speeds you are getting.

I've streamed to all 3 of my Shields simultaneously over gigabit ethernet no problem from my NAS, but haven't tried wifi as it's only 2.4GHz. Router is a Mikrotik RB2011UiAS-2HnD-IN.

Assuming you mean how many devices can be connected and running - not how many instantaneous streams (since that's mainly ISP/bandwidth related):

I have not yet had any issues with my router. RT-AC87U with 2 RP-AC56's spread internet throughout my house and yard, on three independent channels.

Between my wife and myself we have (just on Android): -4 Android cell phones (2 personal, 2 work) -2 Android tablets -1 Chromebook -3 Chromecast -1 Android TV (Sony) -3 Nvidia Shields

We have also had several friends over and never had issue. In addition to that, other constantly-connected devices include: -2 work laptops, 2 surface pros, 1 desktop pc, 3 ip-controlled receivers, 5 DirecTV receivers, 3 Roku boxes, 1 Roku TV, 2 Alarm panels, Lutron smart bridge, Arlo smart bridge, Arlo Q, PS4, an HP Printer ... the list goes on and on.

We're on a 50/50 connection. I've never had issues with DHCP, dropping, cross-talk, ping.... Get a good router, set your channels up so they don't interfere with each other (or your neighbors) and put that router in the ideal location.

Kind of an odd question, but let's suppose you're transferring a file to your Android TV device at 50MB/s somehow and also streaming 4K at 25mbit... then you'd need 400+25 Mbps for each Android TV doing those two tasks. So with a gigabit network, that's two devices. (actual throughput load varies from router to router, but for consumer devices I would assume they don't plan for a workload over 1Gbps)

If you're only streaming 5Mbps HD content on each device, then obviously you have a lot more bandwidth available for each device.

In reality, this isn't really specific to Android TV devices. Any device on your network that's sending packets (smartphone, tablet, desktop, laptop, Rasp Pi, surveillance cam, Smart TV, Smart blu-ray player, any smart appliance, etc.) will be bombarding your router. So in that regard, bandwidth and collisions is a huge variable from network to network, so I can't really answer the question without a lot more detail.

As far as router range due to walls, that's another case of "well, what does your environment look like?" No one can give you a specific answer. At best, we could assume anywhere from zero to 255 devices.

For a specific example, I have an R7000 router and have most of my devices hardwired. My wifi probably serves a couple smartphones and a tablet, with 8 devices plugged into a switch being fed into a LAN port on the router. Never had an issue.

So here is my recommendation, very simple:

If you can somehow run a wire up into your attic and behind your TV to your androidTV devices DO IT. The minute somebody starts doing something crazy on the network (torrenting for example), WIFI is usually the first thing to bug out. Ethernet will usually always be fine - even on old routers.

For me, I can stream netflix / movies on many devices (4-5) at a time with no issues - but the minute I jump on the computer and start doing some heavy downloading / gaming then all the wifi devices will start to slow. The Ethernet devices will be fine.

Take a 4k Blu-ray file and stream it to all your devices. If your home network handles it, you're good.