You can certainly add fields. Just Open Manage | Database | Fields and you can continue to add fields.
However, from what you describe, you are attempting to view all these fields while in table view. There is an upper limit as to how many columns you can see at one time in table view and you appear to have reached this limit. The exact number of columns you can view depends on the number and width of the columns already visible. If you can make your columns a bit narrower, you can squeeze in a few more.
Ultimately, you'll need to modify your design so that you don't have so many columns in one layout. You can create several layouts--each displaying a portion of the total columns. You may also want to consider a redesign of your system. You should also consider whether a redesign of your layouts and tables might eliminate the need for so many columns in the first place.