I've bought two new characters and would like to add them to quest mode play but I can find no option to add them to the starters. Is this not possible or am I missing something?

Make sure you're not checking just experienced characters (left top) when selecting party members for quest.

There is no option to make a new group for quest mode only story mode.

No there is not. You just ad new characters to the "old" team.

Or you can just drag those new characters to the team and leave old out and develop the new characters to the same level as the old ones and then put all of those to the same team.

I found it I just needed to go past the screen where I thought it might be to choose extra characters. Thank you for the responses.