Yes, but as mentioned, each line attracts a rental fee.
I did it at my previous home, and had 2 phone lines for a month. Basically the initial phone line was terrible quality, so I couldn't get ADSL. They wouldn't replace it though, and suggested it could take a few months since it wasn't a high priority. However, Telkom won't say no to new business. So I ordered a second line, and since it couldn't be piggy backed on the previous line due to its poor quality, they had to lay a new line. I then immediately cancelled the first line after installation of the second, since I now could get ADSL. Whole thing took 1 week
Once had 2 ADSL line into home, back in the day when 1mbps was king. Had a motherboard with 2 LAN ports. One 384 line was for the family main LAN, while the other 384 lines router was only plugged into my second LAN port and when I wanted to game online and such I'd just disabled the one LAN port and activated the other, then the others online stuff didn't interfere with my gaming.
I have two lines. The one is currently disconnected at the exchange though. At the time I was running a business from home and the max I could get was 4meg. With the kids streaming media all the time and chowing all the bandwidth, the cheapest option was to get another line.
This was many years ago, so can't remember the whole process, but I don't remember having issues with the application. I think I may have done it over the phone or online. You could also try going to a local Telkom shop.