Yes ...stacking batteries (like 4 in series) will ADD voltage. Not good. However..if you can find the correct physical battery size with 1/4 of the voltage (1.35-1.4 v) and stack tbose, you could be OK, but I digress.
Mercury batteries, as you may know, are no longer made due to concern for the environment. For what it's worth, that battery, Exell s27px 6V, I believe might be a silver battery - a long lasting battery. So that you aware , an over- voltage of 0.4 v for some (beefier) cuircuits is no big deal. In some circuits, it could prematurely burn out an element or amp circuit if there is one inside.
Perhaps you can post the name and model of microphone in your next thread. that way it can be researched. That way there'd be no guessing.
DO NOT stack 6v batteries. If you stack them in series you will add the voltage together (6v + 6v) ...with bad results. If you put them in parallel (linked across the terminals) they will not fit the space of the mike battery section and would only increase the capacity and current.
You could be OK with a 6v battery of the right physical size.
I know for a fact that 5.6 volt batteries are available. You might need to go where camera products are available. I have a 5.6 v battery in one of my light meters. Post the mike name and model number and we can narrow this down.