I don't think there was anything related to the Philippines but there were a couple with regards to Venezuela about the turn of the century. I.e. the Venezuelan_crisis_of_1895, which saw some posturing by the US President and possibly could have led to a war if say the government in Venezuela had possibly done something stupid thinking they would get US support. Also later on you had the Venezuelan_crisis_of_1902, which saw the country blockaded by Britain, Germany and Italy for several months over a debt default. According to the general wiki entry Cipriano_Castro who became dictator in 1899 seems to have been something of a disaster for the country and caused not only the debt crisis of 1902 but also a clash with the Netherlands, Dutch_Venezuelan_crisis_of_1908, as well as serious internal problems.
Castro seems to have misjudged the US reaction in 1902 as he thought the European reaction would lead to US intervention on his behave but President Roosevelt decided that the Monroe Doctrine only applied in questions of European states gaining control of territory rather than issues such as debts. Possibly if McKinley hadn't been assassinated you might have had a more extreme US reaction which might have lead to war with the three European powers. Or if someone like Castro had been in power in 1895 and been a lot more aggressive then you could possibly have had a war between Britain and the US as a result.
Only other issue in this period might have been the settlement of the border between the US and Canada in the west where there were disputes over the Alaska_panhandle and as usual there were hotheads in the US arguing for extreme claims up to cutting off Canada pretty much from the Pacific. This was settled by arbitration but possibly if Washington had refused or Britain had been willing to support Canada more?
There are a couple of other issues that might have caused tension Either if Britain had a closer relation with the monarchy in Hawaii and opposed the coup by American planters in 1893 I think it was or had opposed the move by the US to break Panama away from Colombia so they could build the canal. However I think those would be highly unlikely,
Well according to one of those links the Germans only really backed down when the local British squadron gave fairly open support to the US. Possibly if it hadn't been there or had a different commander and that hadn't happened you could have got a German-US war or at least a clash. Possibly not intentionally but with tensions rising it only needs someone making the wrong maneuver or firing a gun and you have a battle starting and both sides blaming the other.
Since we have the Boxer crisis shortly due to occur in China its going to make co-operation between those two powers rather difficult even if their made peace by then. If they were still at war and hence unable to take part Germany might never gain the Tsingtao. - Actually wrong checking here Germany seized the location in 1898 so that was before the Boxer Uprising but possibly war with the US may change this.
That leaves Canada from 1890 to 1898 when the United states won against Spain and got control of Cuba, Philippines and Guam and Porto Rico.
I've read the U.S. had no intention to conquer or incorporate parts of Canada. So when the U.S. Army would cross the border, probably they attack the cities close to the border.
I suspect that would be the view of a lot of people but there were still the hard liners who wanted to 'complete' the revolution by taken Canada 'away' from Britain despite it being totally self-governing and largely independent by this time. Plus once you have troops on the ground and have made enemies its often easier to decide you need to stay to protect your borders. This presumes of course that the US wins that war which may not be the case.
Found this, as it is about the 1890 to 1895 period the article mentions, it is interesting to read:
The four decades l860-l900 were essentially periods of experiment: that new types of ships were continually being evolved, to serve a comparatively short time, to be discarded and superseded by something newer, this latter also immediately finding a successor, until our fleets, when collected together for grand manoeuvres, presented tlie most amazing variety of types, so far as large armoured ships were concerned. During this time a large amount of money was always expended on smaller ships- frigates, corvettes, and gunboats in the earlier period, cruisers, torpedo boats, and destroyers in more recent years. In the sixties, the seventies, the eighties, and the nineties (to a smaller extent) the British fleet abroad was much larger.
Before the year 1890, although the larger units of the fleet were built in batches of two, three, and four ships of the same tonnage and armament, there was no coordinated effort to attain homogeneity and standardization in our battle fleet. The year 1892 marks what may be termed the modern period, as in that year the Royal Sovereign class of eight ships was begun and these ships formed the precursors of a whole line of similar vessels, also built in batches, which in their main features closely resembled one amther. Without entering into tedious details it is sufficient to say that the Royal Sovereigns were ships of 14,150 tons, and that their main armament was four 13.5 in. guns, disposed in pairs, one at each end of the ship in barbettes, with a secondary armament of ten 6in. quick-firing guns on the broadside. They carried in addition sixteen 6 pounders, twelve 3 pounders, and eight machine guns. They were a great advance not only in power but in speed on all the big ships by which they had been preceded, and possessed the advantage, so important in a battle squadron, of complete homogeneity. Ships which have the same speed and the same turning circle can act together in battle in a manner impossible to the same number of vessels of diverse types.
This system evolved in 1892 was continued, due regard being paid to the progress of ordnance, armour, and torpedoes. What is noticeable in the period under review, however, is that in spite of retrogression here and there in the tonnage of our battleships the trend had generally been upwards. Thus the Inflexible 1881, the monster ship of her day, was 11,880 tons. Incidentally it may be remarked that she was rigged as a brig, that is to say with two masts and square yards of immense size, which when sail was made upon them in a strong breeze rendered her completely unmanageable. In 1890 came the Nile and Trafalgar of 11,940 tons, and then the Royal Sovereigns.
In 1889 there advened, under strong public pressure, the passage of the Naval Defense Act, which enabled the British Admiralty to begin the five years' program of shipbuilding, with the immediate construction of 10 large battleships, 42 cruisers, and 18 torpedo destroyers.
In introducing this policy to the House of Commons, Lord George Hamilton made the following statement :
"Our supremacy on the sea must, after all, be measured by the number of battleships we can put into line. It is further our duty, as we find other nations pushing forward this particular class of ship, to do the same. I have endeavoured during the past year to study the speeches of those who, in previous years, have held my position and that of Prime Minister, so as to ascertain the paramount idea underlying their utterances when they spoke of the standard of strength upon which our naval establishment should be maintained.
"I think I am accurate in saying that our establishment should be on such a scale that it should at least be equal to the strength of any two other Countries.
"I notice that the right honourable gentleman the member for Edinburgh (Mr. Childers) has given expression to that view, and has stated that he felt certain that when he left the Admiralty the British fleet was equal to the combined forces of any two other countries. That may be the case, but it must be borne in mind that at the time of which the right honourable gentleman speaks, there was only one considerable naval power in Europe, while the feature of the present situation is that there are now not one or two, but four or five nations which are spending largely on their naval armaments."
In 1893-4, Mr. Gladstone was Prime Minister. Mr. Gladstone's Ministry held that the reduction of expenditure upon defence was an act of moral virtue ; whereas Lord Salisbury's Government merely waited to be convinced of the necessity of increase, before doing their duty. Nevertheless, the Navy Estimates of March, 1894, provided for an expenditure of no less than 30-1/4 millions upon new construction spread over five years. The Spencer program, as it was called, not only provided the ships required, but included a scheme for manning them. It included a comprehensive program of naval works in which, for the first time in history, the defence of the Empire was treated as a whole.
By this time the Continent was divided between the the Dual Alliance [formed in secret negotiations from 1891 to 1894] of the French Republic and Imperial Russia, and the opposing Triple Alliance [formed in the spring of 1883] of Imperial Germany, the Austro-Hungarian Empire, and the Kingdom of Italy. The enormous naval armaments of England were at first not imitated at the same ratio by Britain's traditional enemies in the Dual Alliance, France and Russia. For while between 1881-1890 the dual powers had built 233,144 tons against England's 196,440, the last decennium, 1890-1900, showed England with 715,150 tons added to her naval strength, against her adversaries' but 495,611.