Can you overtest or over-assess students?

Yes, it's possible to overtest or over-assess students. When the main metric is testing, then both students and teachers tend to cater all of their learning toward what will be on the test. This was a major issue with regular standardized testing, as teachers began to teach solely to the test, both for job security and to meet goals.

How much becomes too much? That line isn't well-defined. However, while it's important to have several formal assessments or tests per year in order to gauge learning over time, such formal assessments are stressful for learners. Both aspects of it have to be weighed.