How to add duplicate keys into the Dictionary

how to allow to add duplicate keys in Dictionary

It is not possible. All keys should be unique. As Dictionary<TKey, TValue> implemented:

Every key in aDictionary<TKey, TValue> must be unique according to the dictionary's equality comparer.

Possible solutions - you can keep collection of strings as value (i.e. use Dictionary<string, List<string>>), or (better) you can use Lookup<TKey, TValue> instead of dictionary.

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how to check for duplicate keys and delete previous value from Dictionary?

You can check if the key exists with previousLines.ContainsKey(dialedno) but if you always want to hold the last line, then just replace whatever dictionary had for the key, or add the new key if it is not in the dictionary:

previousLines[dialedno] = line;

We can Use a List of Key Value Pair

List<KeyValuePair<string, string>> myduplicateLovingDictionary= new List<KeyValuePair<string, string>>();
KeyValuePair<string,string> myItem = new KeyValuePair<string,string>(dialedno, line);
myduplicateLovingDictionary.Add(myItem);