Please add filters that allow us to change the Authorize Net gateway account based on branch, as you had did for Stripe accounts before:

add_filter('wppizza_gateway_stripe_filter_options', 'myprefix_filter_stripe_options', 10, 3);
function myprefix_filter_stripe_options($gateway_options, $order_details, $filter_ident){	
/* 
same *unique* identifier set for the formfield
*/
$unique_ident = 'shop_branch';
/*
values branch 1
*/
if($order_details['customer'][$unique_ident]['value'] == 'Branch 1' ){
/*
set Stripe API keys as required for Branch 1
edit as required 
*/
$gateway_options['LiveSecretKey'] = 'sk_live_someapikeybranch_1';
$gateway_options['LivePublishableKey'] = 'pk_live_someapikeybranch_1';
$gateway_options['TestSecretKey'] = 'sk_test_someapikeybranch_1';
$gateway_options['TestPublishableKey'] = 'pk_test_someapikeybranch_1';
$gateway_options['WebhookLiveKey'] = 'whsec_someapikeybranch_1';
$gateway_options['WebhookTestKey'] = 'whsec_someapikeybranch_1';
}
/*
values branch 2
*/
elseif($order_details['customer'][$unique_ident]['value'] == 'Branch 2' ){
/*
set Stripe API keys as required for Branch 2
edit as required 
*/
$gateway_options['LiveSecretKey'] = 'sk_live_someapikeybranch_2';
$gateway_options['LivePublishableKey'] = 'pk_live_someapikeybranch_2';
$gateway_options['TestSecretKey'] = 'sk_test_someapikeybranch_2';
$gateway_options['TestPublishableKey'] = 'pk_test_someapikeybranch_2';
$gateway_options['WebhookLiveKey'] = 'whsec_someapikeybranch_2';
$gateway_options['WebhookTestKey'] = 'whsec_someapikeybranch_2';		
}
/*
... etc etc ....
*/
return $gateway_options;
}

Thank you