Why would you want to use a single handler instance against multiple
loggers? It's safe to do so, but you could get duplicated messages
appearing. I presume you have reviewed the documentation and are aware
that loggers are organised in a hierarchy and that in the normal case,
handlers of all parent loggers are allowed to handle events logged with
a particular logger.

What do you mean by "single stream in multiple handlers"? In general
this could result in garbled output, if you have multiple threads in
your environment.

Are these questions relevant to this SysLogHandler issue? I couldn't see
a connection with your earlier comment. If not relevant, please post
them on comp.lang.python where you will probably get more people looking
at them, so that the quality of answers is likely to be more helpful to you.