You can, but why would you want to?

You will end up with neither one or the other.

If it is to save on compost in containers, then fill the bottom two thirds with the old compost (providing it is not diseased) and the top third with new.

This method is more likely to give you more success rather than mixing them.

I've got a big pile of spent compost in my garden which i will happily use for my tubs etc. I will usually mix it 50/50 with new stuff and add some growmore to it.

Don't forget that new compost only has enough nutrients in to last 6 weeks before before you need to start feeding

If you wish to rejuvenate compost go for chempak BTD.
That has a better formula than growmore, plus essential trace elements that growmore doesn't have.
Proper peat compost, unlike that you buy from garden centres/DIY stores, from experience,will feed for longer than 6 weeks.
My dahlias have been in 5" pots for more than 6 weeks they are heavy feeders , and have not been fed.
My sweet peas spent 4 months in the same compost without feeding.
However, if you assume your compost will only last 6 weeks, you can always add extra BTD and it will last for 12 weeks:)

Thanks for the advise