Hello All, 
I have reproduce  your code from the 
Read Multiple BME280 Sensors —TCA9548A I2C Multiplexer
example. 
I did it with a PCA9546, ( 4 channels)., with two bme280. 
 

#include <Wire.h>
#include <Adafruit_Sensor.h>
#include <Adafruit_BME280.h>

Adafruit_BME280 bme2; // I2C
Adafruit_BME280 bme3; // I2C

// Select I2C BUS
void TCA9548A(uint8_t bus){
Wire.beginTransmission(0x70); // TCA9548A address
Wire.write(1 << bus); // send byte to select bus
Wire.endTransmission();
}

void printValues(Adafruit_BME280 bme, int bus) {
TCA9548A (bus);
Serial.print(“Sensor number on bus”);
Serial.println(bus);
Serial.print(“Temperature = “);
Serial.print(bme.readTemperature());
Serial.println(” *C”);
 
Serial.print(“Pressure = “);
Serial.print(bme.readPressure() / 100.0F);
Serial.println(” hPa”);

Serial.print(“Humidity = “);
Serial.print(bme.readHumidity());
Serial.println(” %”);

Serial.println();
}

void setup() {
Serial.begin(115200);
 
// Start I2C communication with the Multiplexer
Wire.begin();

Serial.println(); // Init sensor on bus number 2
TCA9548A(2);
if (!bme2.begin(0x76)) {
Serial.println(“Could not find a valid BME280 sensor on bus 2, check wiring!”);
}
Serial.println();
 
// Init sensor on bus number 3
TCA9548A(3);
if (!bme3.begin(0x76)) {
Serial.println(“Could not find a valid BME280 sensor on bus 3, check wiring!”);
}
Serial.println();
 
}

void loop() {
//Print values for sensors
printValues(bme2, 2);
delay(1000);
printValues(bme3, 3);
delay(5000);
Serial.println(” end of loop”);
}

 
It starts to work, but reboots  on the second loop (see below). I tied with a ESP32 Nodemcu board, and
with a ESP8266 Nocemcu board, with the same results. 
 
Any help will be appreciated. 
 
 

Sensor number on bus2
Temperature = 22.43 *C
Pressure = 1023.82 hPa
Humidity = 49.03 %
Sensor number on bus3
Temperature = 21.88 *C
Pressure = 1023.67 hPa
Humidity = 49.75 %
end of loop
Sensor number on bus2
Temperature = 183.89 *C
Pressure = -116.22 hPa
Humidity = 100.00 %

————— CUT HERE FOR EXCEPTION DECODER —————
Exception (3):
epc1=0x4010084d epc2=0x00000000 epc3=0x00000000 excvaddr=0x4003bff9 depc=0x00000000
>>>stack>>>
ctx: cont
sp: 3ffffdb0 end: 3fffffd0 offset: 0150
3fffff00: 00000568 000000ad 3ffe85e4 40100906
3fffff10: 40202c44 3ffe889b 3ffee7b8 3ffee838
3fffff20: 3fffdad0 00000020 3ffef71c 40100c54
3fffff30: 40202c44 00000000 3fffff50 40201532
3fffff40: 3fffdad0 00000000 00000054 40201242
3fffff50: 3ffef71c 00000000 00000000 00000000
3fffff60: 00000000 00000000 00000060 000e5dc7
3fffff70: 00000000 68006d3a 93160032 0bd0d628
3fffff80: fff71835 26acfff9 10bdd80a 0171004b
3fffff90: 012f0000 001e0032 00000000 000000ed
3fffffa0: 000000a0 00000000 3ffee80c 3ffee838
3fffffb0: 00000000 00000000 3ffee80c 402035e0
3fffffc0: feefeffe feefeffe 3fffdab0 40101001
<<<stack<<<
————— CUT HERE FOR EXCEPTION DECODER —————
ets Jan 8 2013,rst cause:2, boot mode:(3,6)
load 0x4010f000, len 3424, room 16
tail 0
chksum 0x2e
load 0x3fff20b8, len 40, room 8
tail 0
chksum 0x2b
csum 0x2b
v00044bc0
~ld
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