At the same time of the day or during the same day, but at two different times - say morning and night.
But the answer is probably no for two reasons.
First, they are both long lasting meds ...12 to 14 hours for Vyvanse and 8 to 10 for Concerta. Thats very close to all day coverage and not necessary.
Second, they are of two different chemical classes. Concerta is a methylphenidate based medicine, while Vyvanse is an amphetamine based med. Usually you go to an amphetamine based because your methylphenidate is not working for you.
The only possible reason I can think of to take both would be to turn off your mind at night so you could go to sleep and stay asleep. But, I doubt that you could find a doctor to prescribe for this.
Hope this helps. Let me know if you need any more info. Best wishes.
Sandman has done an expert job of explaining why these two medications taken together may not be the best choice although that is always to be discussed with your doctor. Here is some information regarding these two medications: https://www.rxlist.com/concerta_vs_vyvanse/drugs-condition.htm
As they are similar in nature and both have overlapping side effects, taking both at the same time has the potential of increasing side effects that both share.
Let us know what your doctor recommended for you.