Is it possible to do Sr. Secondary course from NIOS after doing BPP+ BA from an Open University?

Already you are a graduate. You are eligible for jobs where the graduation is the requirement. You can do B. Ed and MA also. I feel going for those courses may be a good decision. So think in those lines. But you are not eligible if 10 + 2 + 3 requirements are asked for. In such case doing Sr Secondary course through NIOS is a good idea, You can get into NIOS and do your XII through this institute. The website of NIOS is https://www.nios.ac.in/. You can go through that site. There is no upper age limit in this institute. You have to select 5 subjects and you have to pass in all the subjects. In these 5 subjects, there should be one language.

You have already acquired the graduation degree through the open university with the clearance of BPP system. On the basis of your graduation degree, you can look ahead for the jobs which requires this qualification.
If you are interested for the post graduation degree, you can enrol for it and with the minimum scoring of 55 percent in your aggregate, you can appear for NET examination conducted by CBSE. Clearing NET, you will be eligible for the post of lecturership subject to your performance in the final interview consisting of experts.
Your continuation of B.Ed degree would be helpful to you in case you would prefer a teaching profession in some schools. This can be persued through distance course even if you are engaged in some other activities finding no time for regular perusal of the course.
In case of requirement of 10+2+3 pattern for the jobs or otherwise, you will have to take up the senior secondary course through the NIOS. You will have to pass in the five subjects including one being language paper.
Hence decision is to be taken up as per your needs.

You have already done graduation from the open university. So, you are eligible for a job on the basis of graduation degree. Moreover, you can go for higher studies like post-graduation, PhD. You can make a career in the teaching field through these studies. Once you should consider about this field.
If 10+2+3 pattern is required then it would be better to go for Sr secondary course through NIOS. There is no age bar for this institute. As per rule, the candidate will have to select five subjects. He has to qualify in all five subjects including one should be language paper.

BPP is an enabling program for admission to BA in an open university. It is not equivalent to 10+2. Once you have acquired BA after BPP then it would be considered as graduate degree and you can quote it wherever a graduation degree is asked as eligibility criterion. I do not think that you have to show your 10+2 for making a career. You can always present your credential as BPP plus BA and that would be applicable for entitlement of applying for a job for you. In that case you need not to go for 10+2 by NIOS.

First of all, thank you everyone for the answers. I really want to have my Sr Secondary certificate first so that I can think of anything else.

With respect to NIOS, I dont know which stream I belong to. Stream 1 or Stream 4. Please advise.