In the project managing view, there are project-specific backup functions that allow you to backup everything or something to be kept somewhere else or to be exported to another project a moment later.
A whole project with its writings, images and other stuff can be wrapped in a zip package with a single button press and if needed, the same zip package can be dragged to the project list in the project list view, where a new project is generated from the contents of that zip package. Please note that this will also regenerate all the image catalogs used by the project, i.e. no attempt will be made to combine the new project with any existing image catalogs in the service.
To be honest, the ability to put multiple projects in a single backup without the backup containing the image catalogs used by those projects multiple times is already available, but the user has to enable such functionality separately due to the potentially high server load. Backups generated in this way can be drag'n'dropped into the project list view as usual (image catalogs would not be duplicated even if multiple projects use the same ones).
If one presses the Shift key during drag'n'drop and targets certain project, no new project will be created, but the solutions of the backupped project will be merged with the target project (including the image catalogs). This is useful, e.g. when one wants to create one big project from solutions that are spread over several other projects.
If you don't need to backup the whole project, but just want to copy collections of writings from a project so that they can be used in another project, you can copy these writings as JSON structured data, which can be passed as input in the importing view of another project. The item moving view would not allow the moving of writings beyond the boundaries of a single project.