When you say one of those files
1.. is it called global.asa?
2.. is it in the web sites root dir where you want to put the 'visitor numbers' value?
I believe (99.9999% sure - perhaps someone else could jump in and confirm this) each web site can only have one global.asa file. If you have three web sites on your web server each needing a global.asa make each web site a virtual directory (IIS setting in the properties of each web site).
If the answer to Q 1 and 2 is yes, this is fine use the same file. A global.asa file can have as much functional code as you like, DB connections, hit counters, application counters, session timeout settings..... (do not attempt to write to a browser inside this file, it has no GUI)
Wind is your friend