Emma
I don't believe the TIF format allows this. If you need to write different resolutions into a single file, NITF or NetCDF formats allow that. But one key reason NOT to do that is you're duplicating data volume, and there's another risk to consider - if you're leaving some of the other files behind, you may lose an important metadata file.
Peter's point is that, if you're working in ArcGIS, there's no need for this - the mosaic dataset can manage all of your separate files and present them to the user as a single image. And if you want to stack 8 multitemporal scenes covering the same area, that can be one mosaic dataset (does not require 8).
Our imagery workflows site http://esriurl.com/ImageryWorkflows provides resources if you want to learn more, or automate these sort of tasks.
Note you mentioned "number of files delivered". You can share a mosaic dataset with colleagues if you're on the same network, or if working in the cloud, we have ways of allowing the mosaic dataset to access all of the necessary source files directly from cloud storage. But our recommendation is that you keep all of those original source files together (in most cases - there ARE cases where we recommend converting original files to more efficient formats - see Imagery formats and performance—Imagery Best Practices | Documentation and if necessary to reformat we'd recommend using http://esriurl.com/OptimizeRasters)
Cody B
