In Classic you can open multiple reports at the same time by browsing to where the reports are and adding them (Open) to the current session. If they are all in the same place you use the usual Windows selection options to select multiple reports and load them on one go.
Alternatively, if you are processing the same reports daily and in the same way that you need the full month output, set up a project and define an export (or maybe two?) to add the result of today's output to the Excel file that you will need at the month end.
If the project had 2 exports you could set one to be your daily report and the other to append to what will be you monthly version of the report.
Either option should work fine - use whatever you feel most comfortable with.
Grant's suggestion will certainly be the most efficient going forward so that you can continuously create your monthly file. Another option to consider if you are having to go back and catch up on your monthly files is to combine the files before importing. You mentioned a "daily printed report" but I can't tell if that means they are print image files, tab delimited text files, PDFs, etc. If they are text files and you have each daily file all within the same folder, you can combine them with a simple batch file.
Open up Notepad and type: copy *.txt all.txt
Save the file within the folder that has your daily files as a BAT file (i.e. Combine.BAT).
Close Notepad and open up the folder where you saved it and double click on the batch file. This will run a script to combine all files that have a .txt extension and put them in a new file called all.txt. Use the all.txt file in Monarch to import everything at once.
This all assumes that you have text files. Alternatively, if they were PDF files, you could simply select them all and use Acrobat to combine them for you.
Hope this helps, feel free to reach out with any questions.