Yes, you could do a similar thing for multiple text fields but you would have to do some custom logic yourself. Create a custom property and property control. The property control needs to convert the multiple strings to either a single string with some separator (like comma) or xml. There is a class, EPiServer.Core.PropertyMultipleValue, that you might inherit from to do some of this for you.
The next thing you have to do is the PropertyDataControl that does the presentation logic for the property (both edit and view mode). If your not familiar with the property concept in EPiServer CMS 5 there is a video that explains some of the possibilities here: http://world.episerver.com/en/Video/DevSummit/Custom-Property-Types-in-EPiServer-CMS-5-/
EPiServer Development Team
I would like to be able to add multiple instances of the same field for a page. So, it should be possible to add multiple textfields (1 to x) to an included picture. I've seen the link collection, and was wondering if something similar could be done for text.
Thanks in advance