If you use separate schedules - they will not stop the other processes from running. Just a suggestion - but using the wizard is confusing (to me).
Instead of using the wizard, just create a new maintenance plan. Then you can create a plan that meets your exact requirements, including multiple sub-plans with separate schedules.
Regardless of how you schedule and build your maintenance (Maintenance Plans vs Agent Jobs) - you need to consider what steps should be taken and when the next step should process.
A generic outline would be:
History Cleanup (separate plan or job) - perform history cleanup for maintenance plans, agent jobs, backup history. This can be run daily, weekly or monthly depending on how you want to manage your history. Set it to keep enough history to insure you can trend appropriately for your organization.
System Database Maintenance (plan or agent job). This will have 3 components - database integrity check for all system databases, backup system databases, remove old backup files. The backup step will only run upon successful completion of the integrity checks.
User Database Maintenance (plan or agent job). This will have 3 (or more) components - with the integrity check, rebuild indexes, update statistics (column stats only), backup and remove old backup files. The dependencies on this will be success after the integrity check - completion after index rebuilds/update statistics - and success between the backup and remove backup files.
You can move the rebuild and update statistics to a separate schedule to be run weekly depending on your maintenance window, the size of the databases, etc... Note: for larger databases you want to implement a process that rebuilds indexes based on level of fragmentation instead of rebuilding all - and use a separate task for updating statistics.
- User Transaction Log Maintenance (plan or agent job). This will backup the transaction logs for all user databases at the frequency you need for each database. Multiple sub-plans/jobs will be created depending on each databases requirements.
This basic outline can then be adjusted for each system - as needed to support the business. For some systems, adding differential backups - switching to weekly full, daily differential for example - will be fairly easy to plug in...
The goal is to insure your databases are backed up...but only if the integrity checks are good. All other steps between the integrity check and the backup should be set for completion - that way if they fail your backups will still execute.