class CustomerTypeField extends \Magento\Checkout\Model\Layout\AbstractTotalsProcessor implements \Magento\Checkout\Block\Checkout\LayoutProcessorInterface
{
    public function process($jsLayout)
    {
        if(!$this->configuration->isEnabled()){
            return $jsLayout;
        }

        $customField = $this->getExtensionAttributeFieldAsArray();

        $newJsLayout = [
            'components' => [
                'checkout' => [
                    'children' => [
                        'steps' => [
                            'children' => [
                                'shipping-step' => [
                                    'children' => [
                                        'shippingAddress' => [
                                            'children' => [
                                                'shipping-address-fieldset' => [
                                                    'children' => [
                                                        \MageSuite\BusinessCheckout\Helper\Configuration::CUSTOMER_TYPE_ATTRIBUTE => $customField
                                                    ]
                                                ]
                                            ]
                                        ]
                                    ]
                                ]
                            ]
                        ]
                    ]
                ]
            ]
        ];

        $jsLayout = array_merge_recursive($jsLayout, $newJsLayout);
        return $jsLayout;
    }
}

class CustomerType extends \Magento\Eav\Model\Entity\Attribute\Source\AbstractSource
{
    public function getAllOptions()
    {
        if ($this->_options === null) {
            $this->_options = [
                ['value' => self::PRIVATE, 'label' => __('Private')],
                ['value' => self::BUSINESS, 'label' => __('Business')]
            ];
        }
        return $this->_options;
    }
}

class SaveCustomerTypeInQuote
{
public function beforeSaveAddressInformation(
        \Magento\Checkout\Model\ShippingInformationManagement $subject,
        $cartId,
        \Magento\Checkout\Api\Data\ShippingInformationInterface $addressInformation
    )
    {
        $shippingAddress = $addressInformation->getShippingAddress();
        .....
        $customerType = $shippingAddress->getExtensionAttributes()->getCustomerType();
        .....
        $quote = $this->quoteRepository->getActive($cartId);
        $quote->setCustomerType($customerType);

        return [$cartId, $addressInformation];
    }
}