Is it possible to have more than one client connecting to python BLE server at once?

Question

I've been testing the bless-library for BLE. This is the server code I've copied:

    import sys
    import logging
    import asyncio
    import threading
from typing import Any, Union

from bless import (  # type: ignore
    BlessServer,
    BlessGATTCharacteristic,
    GATTCharacteristicProperties,
    GATTAttributePermissions,
)

logging.basicConfig(level=logging.DEBUG)
logger = logging.getLogger(name=__name__)

# NOTE: Some systems require different synchronization methods.
trigger: Union[asyncio.Event, threading.Event]
if sys.platform in ["darwin", "win32"]:
    trigger = threading.Event()
else:
    trigger = asyncio.Event()


def read_request(characteristic: BlessGATTCharacteristic, **kwargs) -> bytearray:
    logger.debug(f"Reading {characteristic.value}")
    return characteristic.value


def write_request(characteristic: BlessGATTCharacteristic, value: Any, **kwargs):
    characteristic.value = value
    logger.debug(f"Char value set to {characteristic.value}")
    if characteristic.value == b"\x0f":
        logger.debug("NICE")
        trigger.set()


async def run(loop):
    trigger.clear()
    # Instantiate the server
    my_service_name = "Test Service"
    server = BlessServer(name=my_service_name, loop=loop)
    server.read_request_func = read_request
    server.write_request_func = write_request

    # Add Service
    my_service_uuid = "A07498CA-AD5B-474E-940D-16F1FBE7E8CD"
    await server.add_new_service(my_service_uuid)

    # Add a Characteristic to the service
    my_char_uuid = "51FF12BB-3ED8-46E5-B4F9-D64E2FEC021B"
    char_flags = (
        GATTCharacteristicProperties.read
        | GATTCharacteristicProperties.write
        | GATTCharacteristicProperties.indicate
    )
    permissions = GATTAttributePermissions.readable | GATTAttributePermissions.writeable
    await server.add_new_characteristic(
        my_service_uuid, my_char_uuid, char_flags, None, permissions
    )

    logger.debug(server.get_characteristic(my_char_uuid))
    await server.start()
    logger.debug("Advertising")
    logger.info(f"Write '0xF' to the advertised characteristic: {my_char_uuid}")
    if trigger.__module__ == "threading":
        trigger.wait()
    else:
        await trigger.wait()

    await asyncio.sleep(2)
    logger.debug("Updating")
    server.get_characteristic(my_char_uuid)
    server.update_value(my_service_uuid, "51FF12BB-3ED8-46E5-B4F9-D64E2FEC021B")
    await asyncio.sleep(5)
    await server.stop()


loop = asyncio.get_event_loop()
loop.run_until_complete(run(loop))

It's avaivable here.

I've tested this with one ESP32-C3-DevKitC-02 and a phone with nRF Connect-app. While both devices can connect and disconnect to the server, they don't seem able do it at the same time. The other client will have to disconnect first.

Would it be possible to connect at the same time in some way with this library? I could also use another one, preferably with permissive license. Is it possible with BLE at all, or do I need the programs to handle connecting one at a time? Or would it be possible to use another low-energy communication protocol? I don't have experience with them much, but I would be willing to learn.