Is it worthwhile to upgrade an old but quality DAC?

I am most interest to seek advice from DAC experts about potentially upgrading an old DAC. I have an old but excellent DAC, Altis Reference. It provides decent sound when connecting to CEC TL0 Transport. When comparing to streaming same music or song using Oppo 105  ( accessing  Tidal Master level file using Oppo which connects to Altis), my CD  provides better quality (both set ups uses decent interconnecting cables). Since Altis DAC can only transmit CD quality resolution 44KHz, I wonder if it can be upgraded to accept higher resolution from streaming (assuming the cost of upgrading is  reasonable  comparing to  buying a new DAC with similar quality sound ). If so, any recommendation of who can do such upgrade? Thank you very much for your advice.

Thank you and appreciate all for your advice. When playing regular CD using Oppo 105 which connects directly to my Doshi preamp, or connect to Altis Reference which then  connects to Doshi Preamp, the quality of sound seems slightly better with Altis connection. When playing SACD, Altis Reference will not transmit the sound  as it only works with 44/16.  Thus I agree it is not worthwhile to upgrade Altis per your advice . 
While on this issue and being naive on digital/streaming, any suggestion from Audiogon experts if sound quality of Oppo 105 can be improved with streaming Tidal Master level music files. In comparison when I connect CEC TL0 to Oppo 105 Coaxial input, the SQ of playing CD is improved quite noticeably. Thus,  I wonder what would be the practical way to improve SQ when streaming with Oppo 105 for the  high resolution source such as Tidal Master level music file? 
I would not say my 105 is reference quality.  My emotiva pre sounds better and my Chord crushes it.  The 105 is great for SACD and theater.
Time for something newer. 
Most good modern dacs will sound heaps better than the 105, which I owned happily for a number of years. If the Altis only modestly beats it on redbook, you've got plenty of opportunity to get something that will be a large enhancement. Cheers,
You could add a reclocker in front of the dac. This might improve the sound. It won't give you 24/96 support. 

It is basically impossible to upgrade an old dac to high bit rate unless the manufacturer says they can do it. Some expensive dacs has the dac chip on a small board the could  be swapped. 

Might be better to buy a new dac.