If I'm already in the U.S. under another lawful status, can I switch to student status if I decide I'd like to study here?

Yes, but the USCIS is often skeptical of such cases. It may suspect that you intended to study when entering on a different visa category. The best defense to this type of accusation is to be upfront when you submit your application for a visitor visa. If you think that at some point during your visit that you may want to attend a university, you can include as part of your application your intent to become a prospective student. For example, you are not sure which university you want to attend or even whether you want to or not. You have, however, narrowed your potential choices to two colleges. You want to get a feel for the campuses and the education environment before you make a final decision. Once you get here, you are inspired and want to enroll immediately. If you declared on your application that you were a “prospective student” up front, you have a greater chance of converting your visitor visa to a student visa. 

In addition to your original intent, timing will also affect your ability to switch from a visitor visa to a student visa. As is the case with most change-in-status applications, your overall status must still be legal. If your visitor visa expired two months ago and you still remained in the United States, you changed to illegal status and will not be allowed to convert to a student visa. If you are close to the end of your visitor visa, a better choice may be to return to your native country and begin a new and separate application for a student visa. Do not risk falling into illegal status, which means staying beyond the time frame authorized by your visa. The illegal status can subject you to immediate deportation, denial of your application to change your status, and denial of re-entry at a later date. Seek the advice of your university's foreign student counselor or an attorney that regularly practices immigration law. They will be able to help you decide which type of student visa is best for your situation and the timing of your application.