Good Things Come In Threes - has a definite positive connotation.

From fairytales to hollywood blockbusters, “the rule of three” (Latin-"omne trium perfectum") principle suggests things that come in threes are inherently more humorous, satisfying and effective than any other number of things.

Other than "bad things comes in threes,is there a saying, adage or expression that convey the opposite message. ?

Solution 1:

It never rains but it pours' may suggest the negative meaning you are referring to.

• something that you say which means that when one bad thing happens, a lot of other bad things also happen, making the situation even worse.

Also:

'Misfortunes never come singly'.

• bad things or situations always come in groups, they never come in a single way.

( from TFD)

Solution 2:

Three Strikes Law

Wikipedia, Three Strikes Law (https://en.wikipedia.org/wiki/Three-strikes_law)

"In the United States, habitual offender laws (commonly referred to as three-strikes laws) are statutes enacted by state governments which mandate courts to impose harsher sentences on those convicted of an offense if they have been previously convicted of two prior serious criminal offenses. They are designed to incapacitate those more likely to commit crime.

"Twenty-four states have some form of "three-strikes" law....."

Appropriated from "three strikes and yer out!" (Baseball)