Yes, this is possible with CRM, but not out of the box. I did something very similar to this with a client. You will need to do some planning and customization's to make it work.
These are the general concepts and architecture, so adjust accordingly.
Assume the user that submits the purchase request is a CRM user, and that users Manager needs to approve it, both of these fields should be available on the System User record. It may require some maintenance to keep it up to date with changes, but
it should be there.
You can put a new status on the purchase record like 'Draft' for when the user is working on the request. When they are ready, they can change the status to 'submit'. You can put a workflow on the entity to look for when the status changes to
Submit, and set the ownership of the record to the users manager, then send the manager an email to let them know they have something to approve.
Put another custom status like 'send to finance', and the manager will set that status if they approve the request. Again, put a workflow on the record that checks for a status of 'send to finance', and change the ownership of the record to the finance team/person.
Send them an email that it's ready for processing.
Good luck!