connect to multiple computers at once

[alextrical]

Is it possible to connect to 2 computers at the same time with one ESP32 to allow sharing a single or multiple mouse signals from a single hardware board. I tried to use the following to advertise 2 Bluetooth mice, but only one is advertised

#include <BleMouse.h>

BleMouse bleMouse("Mouse 1");
BleMouse bleMouse2("Mouse 2");

void setup()
{
  bleMouse.begin();
  bleMouse2.begin();
}

void loop()
{
}

Is there any presidency for advertising a second device.