You can just update your list of sObjects, SF is capable of doing it. Just make sure that the elements in your collection are sorted per object type and not chaotic. Chunking will only allow you to have up to 10 chunks for the DML, and each chunk is up to 200 records of the same object type.
So, for example, if you have 201 Accounts, 50 Leads and 399 Contacts in your list, you will use 5 chunks out of allowed 10. This will only be true if the list is sorted/ordered by object type. So if you would have a list like [Account, Lead, Contact, Account, Lead, Contact, Account, Contact, Account, Lead, Contact, Lead, Contact, Account, Lead], then update on your list will fail because the first 10 records will use all 10 of the allowed chunks.