No, you can't use Optional Practical Training a few years after graduation. It's not even allowed to be taken a year after graduation. Post completion OPT should be applied for as early as 90 days before graduation and not later than 60 days after graduation. Waiting for a long time will take away your eligibility for OPT.
The best thing for you to do if you want to stay in the US is to take your OPT right away so you can work legally for 12 months. If your field of study is in Science, Technology, Engineering and Math, then you are eligible for 24 months extension of OPT. During the 36 months of OPT, you can change employers as long as the new position is still related to your major.
After the validity of OPT, however, you must obtain a new non-immigrant visa. You can either continue with an F-1 visa and do Master's or PhD studies or get a working visa like H-1B or O-1 visa. If you choose to do higher studies, you can take another 12 months of OPT for Master's and another 12 for PhD.
Note: This is not a legal advice.
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