What is the latest position on pursuing two degrees simultaneously in India?

Yes, we can pursue two degrees simultaneously but here it is a catch. We can take up one as a regular course from a recognised university and the other one, in that case, would be from the distance mode offered by some other university fulfilling its recognition status in accordance with UGC norms.
Probably restriction of continuing two regular courses from the same university or from other regular university might be due to the fact that taking up such a venture might produce unnecessary strain to the aspirants in their engagements for two courses simultaneously.
Hence the aspirants can proceed for the regular course from a recognised university and get enrolled themselves for continuing the other course through the distance mode, of course, from a recognised university.
The following are some of the notable universities providing us courses through the distance mode having their recognition status through UGC-
1) Indira Gandhi National Open University.
2) Karnataka Open University.
3) Manipal University of Distance Education.
4) Utkal University.
5) Nalanda Open University etc.
The aspirants have to enrol themselves for one of such open universities for the permission and continue studies through the distance mode with clearing the papers partly or fully as per their convenience.
Scholarship would depend upon the performance of the aspirants and also as per provision of the university regulations.

Yes, you can take two degrees simultaneously but are not allowed to pursue both of them in regular mode. You can take one in regular mode and the other through distance learning mode. For a better answer refer, to https://www.indiastudychannel.com/experts/48152-pursuing-masters-of-various-streams-together. There you can get various explained alternatives.

There is a rule of UGC that you can't take two degrees simultaneously in regular mode. For pursuing two degrees simultaneously, you have to take up one degree as a regular course from a recognized university and another from a distance mode. Nowadays, many universities offer courses in distance mode. IGNOU is a reputed institute that offers various courses in distance mode. You can apply here for a degree in distance mode.

Recently UGC gave clearance for taking two-degree courses simultaneously. But practically it is difficult to attend classes regularly for both courses. Hence UGC allowed students to have one degree in regular mode and the other in distance mode or online courses. If you want to do two courses simultaneously, the effort you have to put in will be very high and you should be able to spare time for learning all the subjects in these two courses. So think twice and then take a decision.

Earlier one regular course and one correspondence or distance learning course was allowed to be undertaken by a candidate during the same period but in a recent stipulation UGC has allowed even two regular courses but there is a condition that their timings should be different and these courses should not overlap with each other.
For example if the classes for one course are in the morning from 8 AM to 1 PM and classes for other course are from 3 PM to 8 PM then it is allowed. Another example is that if classes for one course are on Monday, Wednesday, and Friday and classes for other course are on Tuesday, Thursday, and Saturday then that is also a viable and admissible arrangement.
The idea is that if a student can take that type of load then let him go ahead with that.
Practically speaking very few students will opt for such a system. Another thing is very few institutions will be able to schedule such timings for their courses.