Dear respected Mitch Mitchell2,
Good day! Thank you for posting to Microsoft Community. We are happy to help you.
I’m sorry you’re having a problem and for the situation you encountered, we deeply understand the inconvenience caused and apologize for it.
As per your description, it seems that you cannot add member in your created Microsoft Planner.
May I know if the scenario above is consistent with yours? If so, we have tested it on our side and we can add new member. We cannot reproduce the same situation as yours.

Firstly, may I know are you access Microsoft planner from Planner portal(https://tasks.office.com )? If possible, could you please upload screenshot for our reference, so we can understand your exact scenario and provide our suggestion in a productive manner, perhaps some related screenshots will be helpful.
Given this situation, we’d suggest you try another browser to check if the same problem will occur.
We appreciate your understanding that sometimes the initial suggestions may not resolve the problem very soon. However, we can work together to narrow down and resolve the situation. So, please kindly provide more information below to let us work further.
1.Do all plans have the same problem? You can add member in other plan to check if the same problem will occur.
2.Do the other colleagues have the same problem?
3.Confirm are you able to create a Office 365 group?
Please understand that our initial reply may not always immediately resolve the issue. However, with your help and more detailed information, we can work together to find a solution.
I'm sorry and I apologize for that.
Appreciate your patience and understanding and thank you for your time and cooperation.
Sincerely,
Waqas Muhammad