First of all congratulations OP on finding a new job in the current job market. You are probably very talented with exceptional qualifications and the other company is very lucky to have you.
Now back to the main topic. If Schwab does offer you a counter offer under highly unlikely circumstances, DO NOT, and I repeat, DO NOT accept it. This isn’t so much a Schwab issue as it is an issue common to all companies. The moment you make it public that you pursued other opportunities is the moment that you got marked. You will be targeted for layoff at worst and your career will stagnate at best.