Actually, insuring more cars relates to a lower risk for insurance companies, not more. The basic idea is that if one person owns more than one car, then the risk to the insurance company for that person's vehicles is reduced by half. Because your insurance rates are based on the risk, your rates may go down, but they are not likely to go up. Your auto insurance provider may even offer you discounts for insuring multiple cars or having multiple lines of insurance through a single company.
On the other hand, each car added to your policy will increase the amount of your premiums. Your rates do not increase, but the number of vehicles you are paying for results in higher premiums. This means that even if having multiple cars results in spending less for the insurance, the cost of the policy will increase solely based on the number of cars insured.
Once you have multiple cars insured, anything that happens with your policy will be applied across the board. If you have three cars and are charged in a couple of accidents in a short period of time, your insurance rates as a whole will increase, but the increase may seem greater because it is applied to all of your vehicles.
It is generally cheaper to insure multiple vehicles, but there are minor increases in the premium for each car added to the policy, which may cancel out the savings. Compare insurance offerings from several different car insurance companies and look for the lowest increase per vehicle that does not fall short on the insurance coverage you need to have.