your best solution would be to create multiple dataflows in the control flow area of your package.
create your first dataflow to move the data to the single table on your new server.
the create the remaining data flows within a sequence container and use the control flow expressions to completetion to ensure your data flows then execute in the correct order .....
alternatively, you may just want to have a second data flow reading of the single table and use conditional splits to split the data into logic paths........
(I don't know your data or it's complexity but is an alternative). Hope that helps
MCITP: Business Intelligence Developer (2005)