The incoming request has too many parameters. The server supports a maximum of 2100 parameters

Simple - as long as TheTAbleID's contains less than 2100 ID's then - it is not legal to do that.

Cut the table into blocks of 2000 and then query each block separately, possibly in multiple threads.

SQL doesn't support more than 2100 values in in statement, but you can use in with table with more than 2100 rows so you can insert your data into a table and change your query to check the in with selecting from that table

for example

Create TempIDs (bigint ID, uniqueidentifier guid)

guid column is for preventing mixing different user data

in your code

Guid myKey = Guid.New();
List<long> TheTableIDs = list of IDs (sometimes more than 2100)
TheDataContext.TempIDs.InsertAllOnSubmit(TheTableIDs.select(i => new TempIDs{ID = i, Guid = mykey});
TheDataContext.SubmitChanges();

var QueryOutput = (from x in TheDataContext.SomeTable

                   where TheDataContext.TempIDs.Contains(x.ID) &&

                   x.Col1.Contains(SomeString) || 
                   x.Col2.Contains(SomeString))

                   select x.ID).ToList();

also if you can retrive the ids from database , you can write a table value function in sql to return the ids and model this function in your code, let say its name is fnGetIds. Then use it in your code as below

var QueryOutput = (from x in TheDataContext.SomeTable

                   where TheDataContext.fnGetIds().Contains(x.ID) &&

                   x.Col1.Contains(SomeString) || 
                   x.Col2.Contains(SomeString))

                   select x.ID).ToList();

Use 2 where clauses:

List<long> TheTableIDs = list of IDs (sometimes more than 2100)

var _QueryOutput = (from x in TheDataContext.SomeTable
    where x.Col1.Contains(SomeString) || x.Col2.Contains(SomeString))
    select x.ID).ToList();

var QueryOutput = _QueryOutput.Where(w => TheTableIDs.Contains(w)).ToList();

For efficiency, you could refactor the code so it only does it this way if list contains more than 2000:

if (TheTableIDs.Count() > 2000)
   // Code Here
else
   // Code Here