To know the possibilities of side-by-side BA course

You cannot proceed two graduation courses simulteneously with the same university in the regular mode. However if you are so much interested to carry on the B.A cours, you can look out such universities offering you courses in the distance mode.
There are numerous open universities allowing to sustain your B.A course via distance - mode. A few such universities are indicated below for your end destination-
1) Karnataka Open University,
2) Utkal University,
3) Kota Open University,
4) IGNOU etc.
Of all the universities with the provision of distance education mode, you may choose IGNOU for the twin reasons firstly they offer you quality materials for the preparation of the examination apart from a session for thirty days in a year to clarify your doubt in course of your studies by the eminent professors. This will help you to strengthen your basics.

Doing two-degree courses simultaneously in regular college from the same university or from different universities is not acceptable in our country. You can do a diploma course and a degree course simultaneously. This is the rule made by UGC. So you can't complete your BA simultaneously.
There is a chance you can do your second-degree course through a distance mode. There are many Universities in our country offering BA by distance education. IGNOU is one of the best universities offering open education in the country. You can try in that course.
But I feel concentrating on one course and coming out with good points is the best way. That will help you in getting a good job or seat for higher studies. Trying two courses at a time is not advisable but getting the best possible marks in one degree and getting a good job is the best policy.

Before going for two courses simultaneously one has to introspect whether one is capable of completing them successfully or may score low in both of the courses if tried in such a mode. This is very important because one should not try such things at the risk of losing percentage which is vital to the future career.

Anyway UGC stipulation do not allow for two regular courses to be taken up simultaneously so one should avoid that. On the other hand one regular and one distant mode course is allowed to betaken up during the same period and one can enrol for the same using this combination. Please note that when you attempt such a combination you must decide your priorities as to which course you will be giving preference and doing more hard work in that to get good score for making a career after completing that. The second course should not prove a distraction for the studies of the first preferred course.

It is not allowed to pursue two regular degrees at a same time. So, you cannot pursue both the degrees together. If you want, you can enroll for any of the course through correspondence.

My concern is, will you be able to pursue both the degrees together? You were trying for BMS admission while you were oursuing BA, it shows that you are more interested in pursuing BMS course. So, it would be better to go for BMS at a time rather than pursuing both the degrees together. Anyways, BMS are having better job prospects than BA, so securing good scores will make you able to fetch a good job after wards.

As mentioned by the members that one cannot pursue 2 degree side by side, in January 2016, UGC issued an order that Students not allowed to pursue two regular degrees together. The only option is that, one can do either of the following which stand valid :
1. One Degree and one PG Diploma/ Diploma/ Certificate course
2. One Post Graduate Diploma and one Diploma/ Certificate course
3. One Diploma and one Certificate course
4. Two Post Graduate Diploma/ Diploma / Certificate course

As per the Distance Education Council (DEC) :
1. Two Degree through regular mode is not valid
2. One Degree through regular mode and one through distance mode not valid
3. Two Degree through distance mode is valid

We may soon be able to pursue multiple degrees simultaneously from different or same universities either through distance mode, online mode or part time mode with the University Grants Commission (UGC). The UGC in 2019, has set up a panel to examine the matter of studying two degree programmes simultaneously. The consultations are being held with different parties to explore the practicability of the idea.

Never do this. You are likely to end up being a jack of many trades, but master of none!! First of all, focus is very important in careers. You must do only one course. After all, only this will fetch you success. Some years ago, from the same Mumbai, you might have heard the story of a girl who lived in a 220 feet house, if one may call it. I guess it is called Jobarpaetti or something like that. Her father was an auto driver who had migrated from Villupuram ago. This is a town 162 kms south of Chennai city. What happened? She was CA number one in the final examination and also overall ranking and she was flooded with so many offers.

Secondly, you need to have a big clarity on what your strengths are and you also need to check for the scope of a particular branch of study. You can do two courses at the same time, but both should fit your line of specialization and they should also interest you.

I will give you a specific example: from the city of Chennai, there are hundreds who take the entrance exam to the Chartered Accountanty or ICWA course after their plus two examination. Simultaneously, they also enrol for the B.Com distance education course of the prestigious Madras University. Since their advanced preparation for the ICWA course is very intense, they easily pass their B.Com degree and then also complete the ACA or AICWA course. Even manufacturing companies recruit them for salaries like right hundred thousand rupees per annum. This is the wisest and most intelligent thing to do. Check your interest and do only one course at a time.

You might have heard about Event Management and the Supply Chain Management courses. Even these courses are too good. You could plan your career, based on your specific interest, but do only one thing at a time. Never jump into the game, believing someone or some advise that may never correspond to job realities and futuristic careers.

All the very best.