Yes, you can. If you use Google CSS, you can verify multiple accounts with your domain name, but you can only claim one account on your domain name. This means that with Google CSS you can only actively use one Merchant Center to serve ads. With any other CSS, including Bigshopper CSS, it works differently. Each domain name can be verified and claimed at all times by a Google CSS Partner. In fact: it is possible to claim multiple Google Merchant Center accounts as a CSS Partner for one domain.
Please note: if you use affiliate marketing, it is also possible for affiliates in your program to verify and claim your domain name. If you don't want to, please indicate this in the terms and conditions of your affiliate program. Bigshopper does not advertise in any country or in any situation with affiliate feeds in the Merchant Center. Other CSS Partners do, please pay attention here. If you work with Google CSS, you can see which CSS Partner has claimed your domain and possibly advertises with your products (whether or not as an affiliate). If you want to check this, you can login to your Merchant Center. Then choose "Shopping ads" in the menu on the left and then select Configuration. You will now see a dashboard with all the CSS's that have claimed your domain name and possibly advertise with your products. If you use a CSS, for example Bigshopper CSS, you will no longer see this dashboard in your Google Merchant Center. You can then create a new Google Merchant Center for free (through Google CSS), where you verify and claim your domain name. If you do this, you will not lose your claim of your Merchant Center that falls under Bigshopper CSS (although you can get a warning). After claiming in the Google CSS Merchant Center (which doesn't have to be active) you can see the dashboard with all the CSS Partners that might advertise your products.