global class BatchCallout implements Database.Batchable<sObject>, Database.AllowsCallouts, Database.Stateful {

Integer successRecords = 0;
Integer errorRecords = 0;
Integer offset = 0;
Integer maxOffset;
Boolean stopCallout = false;
String endpoint;

global BatchCallout(Integer maxOff){
    maxOffset = maxOff;
}

global Database.QueryLocator start(Database.BatchableContext BC) {

}

global void execute(Database.BatchableContext BC, List<SObject> scope) {
    if (offset <= maxOffset){
        //make callout
        Http h = new Http();
        HttpRequest req = new HttpRequest();
        req.setMethod('GET');
        req.setEndpoint(endpoint+'?offset='+offset);
        HttpResponse res = h.send(req);
        if (res.getStatus() == 200){
            Map<String,Object> results = (Map<String,Object>)JSON.deserializeUntyped(res.getBody());

            //increment offset
            offset++;

            //make DML
            insert records
        } else {
            //make callout with same offset
            //reinvoke execute method ???
        }
    }
}

global void finish(Database.BatchableContext BC) {
    System.debug('Records success: '+successRecords);
    System.debug('Records error: '+errorRecords);

public void execute(Database.BatchableContext context, List<SObject> records)
{
    // perform callout

    // perform DML
}

public void execute(Database.BatchableContext context, List<SObject> records)
{
    // perform callout 1
    // perform callout 2
    // perform callout 3
    // perform callout 4
    // perform callout 5

    // perform DML
}