If I understand your question correctly, you are considering removing the jack posts or lolly columns from under the beam in your basement. This is not a do-it-yourself project and should not even be considered without consulting a structural engineer. There are many factors that have to be considered, some of which include type of current structure, condition of current structure, weight of the current structure going all the way up to the roof line, wind loading, snow loading, and on and on before a structural engineer could determine if it was feasible to consider a change. And then he would have to determine how to replace the support offered by the columns. Changing any of the load bearing features of your house without this is an invitation to disaster.
If you are considering finishing your basement, there are many ways that you can box around these important structures and disguise them. You might want to consider these first.