Cannot connect third device to AppleTV via Bluetooth

Question

I am setting up an app that uses up to 3 external iPhones as controllers via Bluetooth. Everything seems to be set up properly, and the first 2 devices will connect properly, but once I try to connect a third iPhone, it refuses to connect to it.

Is there some limit or some problem with my code? Why can't the third device connect?

- (void)centralManager:(CBCentralManager *)central didDiscoverPeripheral:(CBPeripheral *)peripheral advertisementData:(NSDictionary<NSString *,id> *)advertisementData RSSI:(NSNumber *)RSSI
{
    NSLog(@"Found peripheral: %@\n\twith data: %@", peripheral, advertisementData);

    //Check advertisement data for UUID
    CBUUID* serviceUUID = [CBUUID UUIDWithString:serviceUUIDString];
    NSArray* serviceUUIDs = [advertisementData valueForKey:CBAdvertisementDataServiceUUIDsKey];

    if([serviceUUIDs containsObject:serviceUUID])
    {
        //Valid controller, connect
        NSLog(@"Valid peripheral, connecting...");
        [self.btManager connectPeripheral:peripheral options:nil];
    
        //Save peripheral as player #x
        if(!self.player2)
        {
            self.player2 = peripheral;
        }
        else if(!self.player3)
        {
            self.player3 = peripheral;
        }
        else if(!self.player4)
        {
            self.player4 = peripheral;
        
            //Maximum players connected
            //Stop scanning
            [self.btManager stopScan];
        }
        else
        {
            //Maximum players connected
            //Ignore and stop scanning
            [self.btManager stopScan];
            return;
        }
    
        if(!_peripherals)
            _peripherals = [NSMutableArray arrayWithCapacity:0];
    
        [_peripherals addObject:peripheral];
    }
}

I am storing the peripheral and calling the connection, but it never actually completes the connection. I have tried connecting each of the iPhone in different orders and all 3 devices will connect if they are player 2 or player 3, but player 4 refuses to connect.

Edit:

The second I disconnect any of the connected devices, the player 4 device will connect.