There is no limit on the number of times that you can take the SAT. On the other hand, you can take the ACT up to a maximum of 12 times.
Ideally, you should aim at attempting the SAT twice. More than four attempts are just a waste of time and energy.
The College Board gives you the option of selecting – by the Score Choice feature – as to which scores you would like to forward to the colleges. Up to six scores are retained in the database.
At times, there might be colleges that specifically require you to share all your SAT scores. While the odd bad day for SAT might remain hidden under Score Choice, your entire history with SAT is laid bare if the college so insists.
To keep it simple, focus on giving a maximum of two attempts for SAT. Make the two attempts count.