Yes, absolutely yes! In fact, it's one of big benefits of working with CSV files. Just make sure to save a project file so that all of the relevant files get opened automatically when you need them. Of course project files require that you use input files that have file names that don't change each time you open the project.
The only caveat is that the files must have exactly the same column headings and structure.
The model that you create will be applied to all of the CSV files simultaneously, just as when you're working with multiple report (text) files.
There are many ways to take advantage of this. You could segregate the data with files for business segments, by fiscal period, by region, you name it. In fact, you can build the files in advance and initially populate them without records (only headings) so that you could build a full year project, for instance, before you have data for all of the monthly files. Then build the project to use all of the monthly files, many of which won't have data (for now). Or what have you. Rather a "set it and forget it" scenario.
Thanks for the info, but how though? Once you have a database open, if you go to File, Database... again, it let's you pick another database, but (as far as I can tell) you can't open another one like you can with reports--only pick another database to use. How can I have a second database open at the same time?