So you are currently doing ten rides per week of 1 1/2 miles each. (your work day effectively splits each 3 mile commute into two rides of 1 1/2 miles each)
That means you are used to doing rides of 1 1/2 miles.
I'd say a goal of doing at least 3 rides per week of 3 miles length would be reasonable. You can do that by adding on to one of the commute rides you currently do, and/or by doing other rides on the weekend for fun.
After a month of that, I would say being able to do three rides per week of at least 5 miles length would be well within do-able.

As you ride more, adding miles to a ride becomes easier and easier to do, physically speaking. It's hardest on your body at first when you are not used to doing any long rides.

Good for you commuting to work!