Yes,you can schedule he same batch class again as the class is different and you can schedule it in an another class as mentioned in the below document:
Yes, technically you can schedule the same job with another name but you should not do it since it might happen that both the instances are trying to update the same record or records at the same time and then it could cause locking issues.
Greetings!
Yes,you can schedule he same batch class again as the class is different and you can schedule it in an another class as mentioned in the below document:
https://developer.salesforce.com/docs/atlas.en-us.apexcode.meta/apexcode/apex_scheduler.htm
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Shirisha Pathuri