If streaming might be needed down the road, then ThreadingMixIn and gunicorn are no good because they just collect up the response and write it as a unit at the end (which actually does nothing if your stream is infinite).
Your basic approach of combining BaseHTTPServer with threads is fine. But the default BaseHTTPServer settings re-bind a new socket on every listener, which won't work in Linux if all the listeners are on the same port. Change those settings before the serve_forever() call. (Just like you have to set self.daemon = True on a thread to stop ctrl-C from being disabled.)
The following example launches 100 handler threads on the same port, with each handler started through BaseHTTPServer.
import time, threading, socket, SocketServer, BaseHTTPServer
class Handler(BaseHTTPServer.BaseHTTPRequestHandler):
    def do_GET(self):
        if self.path != '/':
            self.send_error(404, "Object not found")
            return
        self.send_response(200)
        self.send_header('Content-type', 'text/html; charset=utf-8')
        self.end_headers()
        # serve up an infinite stream
        i = 0
        while True:
            self.wfile.write("%i " % i)
            time.sleep(0.1)
            i += 1
# Create ONE socket.
addr = ('', 8000)
sock = socket.socket (socket.AF_INET, socket.SOCK_STREAM)
sock.setsockopt(socket.SOL_SOCKET, socket.SO_REUSEADDR, 1)
sock.bind(addr)
sock.listen(5)
# Launch 100 listener threads.
class Thread(threading.Thread):
    def __init__(self, i):
        threading.Thread.__init__(self)
        self.i = i
        self.daemon = True
        self.start()
    def run(self):
        httpd = BaseHTTPServer.HTTPServer(addr, Handler, False)
        # Prevent the HTTP server from re-binding every handler.
        # https://stackoverflow.com/questions/46210672/
        httpd.socket = sock
        httpd.server_bind = self.server_close = lambda self: None
        httpd.serve_forever()
[Thread(i) for i in range(100)]
time.sleep(9e9)