Multiple domain names and Google

I have a client who has around 16 domain names all relating to the 3 areas of her business - some with the .co.uk and .com equivalents.
I have launched a website for her with her main domain name and this site covers all 3 business areas on separate pages.
My gut feeling is that Google wouldn’t be overjoyed at having 16 domains pointing to the same site - even if they are relevant, but can anyone confirm this or tell me if I have got it wrong?
We would be pointing some of the domains to different site pages.

I don’t think it would be a problem. There are many reasons why a website may want to have several ‘alias’ domains all pointing to the same place – for example, registering multiple TLDs and similar domain names to minimise the risk of cybersquatters hijacking traffic, consolidating several old websites into one new one (eg after a restructure or takeover), promotional branding that is no longer required. As long as all of the domain home pages and other extant URLs point to a relevant page, you should be absolutely fine.

Will all domains forward to one domain, or will each domain show the content as if it belongs at that domain? The only isue you’re looking at here is duplicate content, so Google thinking all 16 sites are identical. I would advise using Canonical links as well to make sure Google (and other engines) know which site should be showing.

They would all forward to the same domain, but some would go to different pages on the website as they would be more relevant to the pages content.
Yip, I always use canonical links. Some of the domains are versions of the main domain eg .co.uk, .com, .net etc but some are related to the 3 different products the site displays

Are you using a 301 redirect for the redirecting of the domain?

Having them all pointing to one site wont harm your main site but it may not help it either. may be worth putting most of them on a host with a different IP address so the connection is not as obvious