Yes, you can participate in the KEAM (Kerala Engineering Architecture Medical) 3rd allotment with higher options if you did not take admission in the college allotted during the 2nd allotment. Here’s a detailed overview of how it works:

1. **Previous Allotment Status**: If you did not secure admission in the college allotted to you in the 2nd allotment, your status will be considered as "not joined" for that allotment. This means you are still eligible for subsequent allotments.

2. **Higher Options**: When participating in the 3rd allotment, you have the opportunity to include higher preference options in your list. By doing so, you increase your chances of getting a seat in a college or course that better aligns with your preferences.

3. **Re-allotment Process**: In the 3rd allotment, the system will first consider candidates who were allotted seats in previous rounds but did not join. If there are available seats in higher-preference institutions that match your new options, you might be allotted a seat there.

4. **Adherence to Procedures**: Ensure that you follow all the procedures and deadlines set by the KEAM authorities. This includes updating your options accurately, paying the necessary fees, and completing any additional documentation required for the 3rd allotment process.

5. **Seat Confirmation**: If you are allotted a new seat in the 3rd allotment, you must complete the admission process at the newly allotted institution to confirm your seat. Failure to do so will result in losing the opportunity.

In summary, your non-admission in the 2nd allotment does not disqualify you from participating in the 3rd allotment. Make sure to exercise your higher options wisely to maximize your chances of securing a preferred seat.