Secret vs TS Investigation

I recently received a favorable adjudication for a secret clearance and am considering accepting an offer for a position requiring a TS. My concern is that I had issues that, though were found to have been mitigated for a Secret, may not be adjudicated favorably for a TS. The issue was primarily alcohol related incidents in the past which has been mitigated in the past few years.

Does the TS investigation go into greater depth (i.e. interview more people) OR does it adjudicate against a more stringent set of criteria (i.e. an issue mitigated enough for a secret may not be mitigated for a TS), or both? If you’ve just recently been granted a secret clearance, how long may this additional investigation take, assuming no material changes to the SF-86?

Also concerned that if the TS investigation finds that an issue is not mitigated enough for a TS, that such a determination may impact my current clearance.

Any input or experience appreciated. Would like to know the risk before pulling the trigger. Thank you.