SQL Find matching entries and return same value if result already exists with ID

So I am currently using a case function that looks at the group an entry is in and returns a result accordingly.

The code I am using looks something like this so far:

Case 
when [Group] = 'b' or [Group] = 'e'
then "Blue"
when [Group] = 'c'
then "red"
when [ Group] = 'd'
then "green"

With that I am getting a table that looks like this

I haven't included a line for when group = A because I only need that group to return it's own result when there's no matching results already. I need entries with the same ID to get categorized into the same result when returning specific values. Is there any way to have the code look for matching ID's and return those results as well given a certain priority level. For example, I need the table result to look as follows:

If I follow you correctly, you can use window functions and conditional expressions:

select id, grp, 
    case
        when max(case when grp = 'd'         then 1 end) over(partition by id) = 1 then 'green'
        when max(case when grp = 'c'         then 1 end) over(partition by id) = 1 then 'red'
        when max(case when grp in ('b', 'e') then 1 end) over(partition by id) = 1 then 'blue'
    end as result
from mytable