IIRC, one of the books on small cruising boats, possibly John Vigor's 20 Small Sailboats to Take You Anywhere, has a long section on beefing up and retrofitting a small coastal cruiser--IIRC, a Catalina 27--to make it seaworthy for such a passage.
It discusses the modifications you'd need to make to such a boat at fair length. Some of the modifications would include adding a bridgedeck to the cockpit, to help increase the seaworthiness and reduce the chances of the boat downflooding and sinking if it gets pooped. Another major upgrade is adding proper backing plates to all the deck fittings, most of which were not backed, but were through-bolted with fender
washers IIRC. Adding seacocks to all the through-hulls was another issue, as some were not equipped with them from the factory.
IIRC, a lot of the information in John's book are based on the work done by Patrick Childress, who circumnavigated in a modified Catalina 27. IIRC, Childress took three months, working full-time, to retrofit/upgrade/modify his boat for his voyage.
That said, I doubt that a Catalina 27 is going to be big enough for more than a single person for a transAtlantic passage, as it doesn't have enough space, stowage or load carrying capacity to handle two people considering the stores you'd need. A rough rule of thumb is that you need ONE GALLON of water per person per day at a minimum. A Catalina 27 will be hard pressed to make 100 miles per day... and the Atlantic crossing is roughly 3000 miles, or 30 days.
For one person that means you will need at least 30 gallons of water aboard. Generally, you'd want at least a 50% safety margin on water, which brings it up to 45 gallons. Ninety gallons for two people. A gallon of water weighs 8.35 lbs., so you need 765 lbs. (rounding it up to 8.5 lbs/gallon to account for the jerry cans) of water for two people. That doesn't include food, clothing, electronics, fuel
for the boat, cooking fuel
, or any other equipment. Figure that two adults will weigh in at 300 lbs. or so.
With two people, you could probably do it... but it wouldn't be a comfortable trip, since you'd be living in each other's pockets.
I would ask what sailing experience you have? It would be rather foolish to try and do this unless you are a fairly experienced sailor, with a wide breadth of boat maintenance and repair
skills. The fact that you're asking the question in your OP pretty much says that you don't have the knowledge, skills or experience to try such a voyage yet.