I have slipped off my bike 3x in the last 2 months - will changing tyres help?
Wet metal plates on the road have an astonishingly low grip, on par with a sheet of ice.
There's very little you can practically change on your bike to improve this - changing to wider tyres at low pressure would help, but the rest of your commute will be like slogging through treacle, and highly unpleasant.
What you can do - change your technique.   Never turn or brake while crossing a metal plate.  Keep the bars and therefore front wheel straight and roll over it.
If the plate is on a corner (and many are)  then try to avoid going over them at all.  Take a left or right position and bypass the plate completely.  Naturally this requires local knowledge and for you to anticipate what's coming up.
It may be possible to participate in activism - write to the local council or similar roading authority, and request the plate be replaced with a textured one, or surfaced with bitumen.  This is a slow process but is not impossible.
Your very last resort is to react quickly should the bike start to slide, and take whatever action helps to restore your balance.  That may be a shift in body weight, which could potentially put you into the path of traffic.  
The counter here is that when your bike is sliding, it happens really quickly and its hard to react in time.
Or find a route that avoids this corner/plate completely.