Does the following help:

;WITH SumPerAcct AS

(SELECT acc_no, SUM(R_Value) AS Sum_R_Value, SUM(time_spent) AS Sum_time_spent

FROM #TESTING

GROUP BY acc_no),

OccurrenceCount AS

(SELECT acc_no, MAX(number) AS maxNumber, c_name, Count(c_name) NumerOfOccurence, ROW_NUMBER() OVER (PARTITION BY acc_no ORDER BY COUNT(c_name) DESC) Sequences

FROM #TESTING

GROUP BY acc_no, c_name),

MaxOccurrence AS

(SELECT acc_no, c_name

FROM OccurrenceCount

WHERE Sequences = 1)

SELECT SumPerAcct.acc_no, OccurrenceCount.maxNumber, MaxOccurrence.c_name, SumPerAcct.Sum_R_Value, SumPerAcct.Sum_time_spent

FROM SumPerAcct --ON SumPerAcct.acc_no = #TESTING.acc_no

JOIN OccurrenceCount ON OccurrenceCount.acc_no = SumPerAcct.acc_no

JOIN MaxOccurrence ON MaxOccurrence.acc_no = SumPerAcct.acc_no

AND MaxOccurrence.c_name = OccurrenceCount.c_name