Adding layers (e.g topo) to my OSM

It would help if you can add a bit more detail about what you've done and what you're trying to do - the "what" of best practices is limited only by your imagination but the "how" is limited by what you're currently doing and what technology you're currently using. A "local OSM server" could be one of many things - for local map editing, tile display, geocoding, clever geo calculations like "how many fast food places in town X are within 100m of a school" or similar.

My apologies.

We have OSM set up in the office on a virtual machine that is currently rendering and displaying tiles, as well as providing some Geocoding for us through Nominatim. What we're looking to do is add additional layers to the standard map, such as the topo maps, so that we can add further detail to the maps. I cannot find much in the way of doing this, unless I'm looking in the wrong place. I just need pointing in the right direction.

I cannot give you a best practice answer. But in the meantime you could take a look at other projects. Opentopomap for example is adding SRTM data to the map and the source is available on Github.