I would be mentioning fully synthetics only, from reputed brands, and meeting latest API SN / SN Plus, and / or ILSAC GF-5 criteria (of course from the brands which I know about
Many many brands are there which I do not know)
0w-20: Caltex Chevron, Total Quartz 9000 Future series, Kixx, ZIC & Shell
5w-20: ZIC & Shell
5w-30: Total Quartz 9000 Future series & Kixx
(These all above mentioned oil grades & brands are confirmed available in Pakistan)
Valvoline, Mitasu, Totachi and Amsoil, all offer 0w-20, 5w-20 and 5w-30, however, regarding availability of 0w-20, 5w-20 and 5w-30 all, by Valvoline, Mitasu, Totachi, Amsoil in Pkaistan, I am not sure.
{Edit: I had forgotten to mention Liqui Moly.
As per http://liquimolypakistan.com/ (the official website), only 01 oil is mentioned in 0w-20 and 5w-30 each (I could not find anything for 5w-20). For 0w-20: http://liquimolypakistan.com/special-tec-aa-0w-20/ SPECIAL TEC AA 0W-20 is there, which is based on synthesis tech. (and is not fully synthetic, because for fully synthetic, Liqui Moly International has a separate category, and this oil is not found there), similarly is true for 5w-30: http://liquimolypakistan.com/special-tec-aa-5w-30/ SPECIAL TEC AA 5W-30. These both are based on synthesis tech. and are not fully synthetic.
For Fully Synthetic motor oils by Liqui Moly, please have a look at: https://products.liqui-moly.com/oils.html?cat=597&oil_type=30
Both of the above mentioned engine oils by LM are not there.}