Based on your further explanation, I think you are making this more complicated than it has to be. You can do the following:
DECLARE @p1 INT = 5, @p2 INT = 3, @p3 INT = NULL;
DECLARE @sql NVARCHAR(MAX) = N'SELECT cols FROM dbo.table WHERE @p1 = @p1';
SET @sql += CASE WHEN @p2 IS NOT NULL THEN N' AND @p2 = @p2' ELSE '' END;
SET @sql += CASE WHEN @p3 IS NOT NULL THEN N' AND @p3 = @p3' ELSE '' END;
EXEC sp_executesql @sql, N'@p1 INT, @p2 INT, @p3 INT', @p1, @p2, @p3;
This will work no problem - any parameters that aren't used in the actual statement are merely dropped and ignored.