Its always hard to help with third party tools - the maker should be your first point of contact to see if performance can be improved with settings or workarounds while dealing with their components.

In many situations cases like this are constrained by the server specs so can you please tell us what they are - including available memory and normal cpu/io load while the packages are executing.

As for the ssis flow - at what point(s) does Melisa gets used? you mentioned 4 tables which could mean that part of the process is done even before passing through Melisa. (which probably is advisable to do if not done already).
if you could either post the package here, or post images of the flow including the exact points that are slow it may help.

General things to look at are
- buffer size
- rows per buffer
- datatypes (are they bigger than what it is required? if so change it as it affects memory allocation by SSIS)
- lookup tables on SSIS - avoid where possible if volumes are big - better to process on SQL

You can also look at splitting the data flow onto multiple outputs onto Melisa and then into same table or multiple staging tables, either can work if table/database are setup for it.