I think Dave is right: first, you need to retro-specify your current system in order to identify what it the business logic that you want to retain. Even though it might be old and clunky, your current system probably embeds a lot of experience and best practices that were developed by your company over the years.
Once you have a clear picture of where you stand, the next step will be to identify what are the features you can improve (or maybe even remove altogether). Ideally, you would also identify the underlying processes and look for new solutions to them.
Let's take a specific example: business expenses. For a long time, people were expected to gather their receipts, fill in an Excel file with the amounts matching those receipts, printing that file, getting it approved and signed, and would be paid at the end of the month with their salary. All this can be replaced by a solution such as Expensify which allows you to take picture of receipts and manage everything online from there.
In summary, what I'd do would be to identify your core processes, then the key requirements for each process. Then I'd look for either a solution that includes most of what you need, or for SaaS applications of record that are interoperable and can help you manage each individual process seamlessly.