The primary meaning of the phrase to give the cat another goldfish, and of its variants, is to spare no expense.

The image is of a spendthrift who feeds their pet cat ornamental fishes.

The earliest occurrence that I have found is from the column Something of Each, by A. F. L., published in The Evening Sun (Baltimore, Maryland) of Wednesday 5^th March 1919:

One branch of the Treasury Department will soon add 350 clerks to its staff. Their yearly salaries will total $1,312,500.
One branch of the War Department will soon add 500 clerks to its staff. Their yearly salaries will total $1,200,000.
The Interstate Commerce Commission will soon add 50 clerks to its staff. Their yearly salaries will total $97,500.
And so it goes.
Think about it all for just a minute and it seems as though what is needed to build up a bureaucracy Germany had and America has. However, what is money to young married people! Tell the wife to give the cat another goldfish and let the tax rate rise!

The second-earliest occurrence that I have found is from the column Andrew and Imogene, by Roe Fulkerson, published in The Indianapolis News (Indianapolis, Indiana) of Monday 14^th November 1927—here, the exact meaning of the phrase seems to be to put all one’s efforts in order to achieve something:

“Oh, Andrew!” exclaimed Imogene. “French tailors are introducing knickers for men to wear to full dress parties!”
“I need no French tailor to introduce me to knickers!” scoffed Andrew. “I’ve met ’em already, on the golf course, on women tin can tourists and on men so skinny that their legs looked like a canary bird’s.”
“But these are to be the fashioned kind, worn with silk stockings and buckled shoes for evening,” explained Imogene. “You would look nice in them, Andrew, you have good legs!”
“Same to you and many of them!” replied Andrew. “About 1850 an English king who had funny legs let his trousers down to his ankles to hide them. Every one in America and in all English-speaking countries followed suit. […]
[…]
“The English started this long pants craze and when we go back to knickers, it will be because the English adopt them. […]
[…]
“If they start wearing knickers to dances in England I will give the cat another goldfish, borrow a pair of black satin stockings, you have stopped wearing, and go to it with the rest of them.”

The phrase occurs as follows in the column In Our Valley, published in The Brownsville Herald (Brownsville, Texas) of Tuesday 26^th April 1932:

Every little bit helps,
As the boy said when he fed the cat another goldfish.

In the account of a baseball match between the Cleveland Indians and the Boston Red Sox, by David F. Egan, published in The Boston Daily Globe (Boston, Massachusetts) of Friday 13^th May 1932, “tossed another gold-fish to the cat” corresponds to “Toss Game Away” in the title, so that the exact meaning of the phrase seems to be to hand victory on a silver platter:

RED SOX LOSE ON A VERY CHEAP RUN
Tie Indians in Eighth, Only to Toss Game Away in Ninth By 5 to 4 Score

The drinks were on the Red Sox again yesterday afternoon, when they lost 5-4 to Cleveland at Fenway Park.
The home heroes spotted Cleveland four runs in the third inning, finally tied up the game in the eighth, and then tossed another gold-fish to the cat in the ninth inning, with a run which was as cheap as a Chinese yen.

The phrase occurs in a letter about Maryland’s relief problem, published in The Sun (Baltimore, Maryland) of Tuesday 26^th February 1935:

Everyone with half a brain knows that relief as administered during the last two years was nothing short of a scandal. Some families had three and four on relief work; other families could not get one on; the local politicians took charge like dogs at a dead horse and wallowed in it. The motto was “Feed the car another goldfish. What do we care for expenses?” . . .

The following is from the column Old Timers, published in the Brooklyn Eagle (Brooklyn, New York) of Sunday 2^nd October 1949:

As Ed Fitzgerald said today: “We are rich, mother. Throw another goldfish to the cat!”

The phrase has also been used in British English. The following, for example, is from a letter by one A. W. Stephenson, living in Hull, published in The Daily Mail (Hull, Yorkshire, England) of Tuesday 20^th September 1949:

Sir,—At the present time we are witnessing an increasing number of transport disputes, unofficial strikes, embargoes on overtime working and a mad scramble for increased wages without a correspondingly improved service or output.
All this in a highly socialised and “trade-unionised” State points to false doctrines and loose thinking. If the workers’ attitude today is a combination of “couldn’t care less,” beggar my neighbour, and “drat the expense, give the cat another goldfish,” who is to blame?

The British author, journalist, editor and publisher Alan John Ross (1922-2001) used the phrase in the account of a cricket match between England and South Africa, published in The Birmingham Post (Birmingham, Warwickshire, England) of Friday 28^th December 1956:

Adcock lunged at his first ball—googly, Chinaman or whatever—and looked up, pleased as a bridegroom, to find it sailing over the midwicket boundary.
That sent up the 200 and Statham, on the principle of “Never mind the money, give the cat another goldfish,” at once called for the new ball. But Adcock was not to be fobbed off after so dashing a start and, with the motions of a man who has heard some inner call to arms, he twice rattled Bailey to the square leg boundary.

According to an article by Betty Berry, published in the State Times Advocate (Baton Rouge, Louisiana) of Thursday 22^nd August 1991, the phrase is used in South Africa to mean to allow oneself more of what one desires—Betty Berry was describing “a typical South African braai, or barbeque” that Linde Hammond, a native South African, organised in her Baton Rouge home for her U.S. neighbours:

Inviting her guests to take seconds, Hammond politely ignored the chorus of “oh, I really shouldn’t,” and invoked a colorful South African expression:
“Go on. Give your cat another goldfish,” she urged, lifting her mother’s silver pot to pour another round of tea. No one turned her down.