Regular grease and synthetic grease are made different using different mixtures of oils so you should not use synthetic grease to mix in with regular grease because it can cause lubrication problems.
Some grease such as synthetic grease and oils are incompatible with mineral oils and other types of synthetic grease.
So although you could mix in some synthetic grease with some regular grease it can cause some problems but if you have to use the synthetic grease with the regular grease in an emergency repair such as on the road with a trailer bearing then it can be okay.
But as soon as you get to where you're going or somewhere where you can clean the grease out you should do so.
Or just remove the old grease as much as you can and then only use the synthetic grease so that it doesn't cause lubrication problems.