Yes you can all another batch job from finish method like below code

global class batchProAssetBuilder implements Database.Batchable<sObject> {
    global Database.QueryLocator start(Database.BatchableContext BC) {
        String myProduct = 'xyz';
        String query = 'SELECT Id,Run_Asset_Builder_Pro__c FROM Account WHERE PIN_Code__c != null AND Product__c = :myProduct';
        return Database.getQueryLocator(query);
    }
   
    global void execute(Database.BatchableContext BC, List<Account> scope) {
         for(Account a : scope)
         {
             a.Run_Asset_Builder_Pro__c = true;            
         }
         update scope;
    }   
    
global void finish(Database.BatchableContext BC){

 // Get the AsyncApexJob that represents the Batch job using the Id from the BatchableContext
 AsyncApexJob a = [Select Id, Status, NumberOfErrors, JobItemsProcessed,
  TotalJobItems, CreatedBy.Email, ExtendedStatus
  from AsyncApexJob where Id = :BC.getJobId()];
 
 // Email the Batch Job's submitter that the Job is finished.
 Messaging.SingleEmailMessage mail = new Messaging.SingleEmailMessage();
 String[] toAddresses = new String[] {a.CreatedBy.Email};
 mail.setToAddresses(toAddresses);
 mail.setSubject('BatchJobXYZ Status: ' + a.Status);
 mail.setPlainTextBody('The batch Apex job processed ' + a.TotalJobItems +
  ' batches with '+ a.NumberOfErrors + ' failures. ExtendedStatus: ' + a.ExtendedStatus);
  
 Messaging.sendEmail(new Messaging.SingleEmailMessage[] { mail });

	NewBatchjob obj = new newBatchJob();
	Database.executeBatch(obj);
 
 }
}

https://developer.salesforce.com/docs/atlas.en-us.apexcode.meta/apexcode/apex_batch_interface.htm

Monitoring a Batch

You can monitor a Bulk API batch in Salesforce.
To track the status of bulk data load jobs and their associated batches, from Setup, click Monitoring | Bulk Data Load Jobs orJobs | Bulk Data Load Jobs. Click on the Job ID to view the job detail page.

Please read below post for same issue
https://help.salesforce.com/apex/HTViewSolution?id=000182449

Description
- Batch Apex can have 5 concurrent (simultaneous) jobs running in parallel.
- That is, explicitly, the number of Batch Apex jobs whose status in the AsyncApexJob table are 'Processing' or 'Preparing'.
- A job is not executing when in Queued or any other status.
- Scheduling more than 5 Batch Apex jobs returns the error "Attempted to schedule too many concurrent batch jobs in this org"
- You may sometimes receive a Developer script exception e-mail when this limit is reached, but not always. (This is also by design).
- You may attempt to use the following code sample to avoid encountering this limit, particularly if the batch is executed in a scheduled class. 

//check if there are 5 active batch jobs
//In some cases, might need to add "Status='Queued' " to the criteria
if ([SELECT count() FROM AsyncApexJob WHERE JobType='BatchApex' AND (Status = 'Processing' OR Status = 'Preparing')] < 5){ 
   Database.executeBatch(batchClassInstance);
} else {
   //schedule this same schedulable class again in 30 mins
   nameOfYourSchedulableClass sc = new nameOfYourSchedulableClass();
   Datetime dt = Datetime.now() + (0.024305); // i.e. 30 mins
   String timeForScheduler = dt.format('s m H d M \'?\' yyyy');
   Id schedId = System.Schedule('MatrixRetry'+timeForScheduler,timeForScheduler,sc);
}

Please let us know if this will help you.

Thanks
Amit Chaudhary