QueryMultiple supports the ability to deal with multiple result sets. The only design restriction we added was totally disabling buffering for the grid reader. This means the whole API is streaming.

In the simplest case you can use:

var grid = connection.QueryMultiple("select 1 select 2");
grid.Read<int>().First().IsEqualTo(1);
grid.Read<int>().First().IsEqualTo(2);

In the slightly more sophisticated case you can do crazy stuff like this:

var p = new DynamicParameters();
p.Add("a", 11);
p.Add("r", dbType: DbType.Int32, direction: ParameterDirection.ReturnValue);

connection.Execute(@"create proc #spEcho
@a int
as 
begin

select @a Id, 'ping' Name, 1 Id, 'pong1' Name
select @a Id, 'ping' Name, 2 Id, 'pong2' Name
return @a
end");

var grid = connection.QueryMultiple("#spEcho", p, 
                                     commandType: CommandType.StoredProcedure);

var result1 = grid.Read<dynamic, dynamic, Tuple<dynamic, dynamic>>(
                  (a, b) => Tuple.Create((object)a, (object)b)).ToList();
var result2 = grid.Read<dynamic, dynamic, Tuple<dynamic, dynamic>>(
                  (a, b) => Tuple.Create((object)a, (object)b)).ToList();

((int)(result1[0].Item1.Id)).IsEqualTo(11);
((int)(result1[0].Item2.Id)).IsEqualTo(1);

((int)(result2[0].Item1.Id)).IsEqualTo(11);
((int)(result2[0].Item2.Id)).IsEqualTo(2);

p.Get<int>("r").IsEqualTo(11);

You'll need to add this using statement to enable QueryMultiple .

using Dapper; /* to add extended method QueryMultiple public static GridReader QueryMultiple(this IDbConnection cnn, string sql, object param = null, IDbTransaction transaction = null, int? commandTimeout = null, CommandType? commandType = null); */

Have you tried the QueryMultiple method? It says it should:
Execute a command that returns multiple result sets, and access each in turn

You'll need to add this using statement to enable QueryMultiple .

using Dapper; /* to add extended method QueryMultiple public static GridReader QueryMultiple(this IDbConnection cnn, string sql, object param = null, IDbTransaction transaction = null, int? commandTimeout = null, CommandType? commandType = null); */

Multiple result set.

var reader = conn.QueryMultiple("ProductSearch", param: new { CategoryID = 1 }, commandType: CommandType.StoredProcedure);
var ProductListOne = reader.Read<ProuductTbl>().ToList();
var ProductListTwo = reader.Read<ProuductTbl>().ToList();

You'll need to add this using statement to enable QueryMultiple .

using Dapper; /* to add extended method QueryMultiple public static GridReader QueryMultiple(this IDbConnection cnn, string sql, object param = null, IDbTransaction transaction = null, int? commandTimeout = null, CommandType? commandType = null); */

Stored procedure:

CREATE PROCEDURE [dbo].[ProductSearch]
    @CategoryID as int
AS
BEGIN
    SELECT * FROM ProductTbl
    SELECT * FROM ProductTbl
END

For me, it was missing one column in my DB table, one of my query is getting exception in QueryMulitpleAsync() due to that missing column.

I will suggest that find the one that blocking you, then compare DB column and your raw query string.