Import of private maps

Your question is likely using terminology that has certain meanings in the context of OSM that you probably don't mean.

Could you for starters explain what you mean by "openstreetmap", the website, the OSM data, a third party application?

If you simply want to -display- data from a third party on top of OpenStreetMap derived maps, you could for example use umap or roll your own web app with Leaflet or openlayers.

If you are building your own mapstyle, you can naturally import the 3rd party data into your rendering database and use from there.

Importing data in to the OSM dataset requires that

• the data is available under a suitable licence
• you have community support for the import
• and the data models fetures or properties that actually make sense in a general purpose geo-dataset

You can find more on that here Import Guidelines but as already said it seems unlikely that that is what you really want to do.