I don't think Earls get 3 titles. It appears it's just Earl and Viscount. The earldoms of Snowdon and Spencer are just Earl and Viscount. You probably have to be a Marquis at least to get 3 titles. A dukedom would definitely have 3 titles.
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The Earldom of Spencer is not just an Earl and a Viscount. There is actually a number of titles in there - Charles Spencer is 9th Earl Spencer, 9th Viscount Spencer of Althorp, 9th Viscount Althorp (Great Britain), 4th Viscount Althorp (U.K.), and 9th Baron Spencer of Althorp.
His ancestor, the 1st Earl Spencer, was first created 1st Viscount Spencer of Althorp and 1st Baron Spencer of Althorp in the Peerage of Great Britain on 3 April 1761. Later, on 1 November 1765 he was created 1st Earl Spencer and 1st Viscount Althorp in the Peerage of Great Britain. Go forward a bit, and in 1905 the younger son of the 4th Earl Spencer, the then Hon. Charles Spencer, was created 1st Viscount Althorp in the Peerage of the United Kingdom in order to become Lord Chamberlain of the Household. His elder half-brother, the 5th Earl Spencer, died with no children, so in 1910 the 1st Viscount Althorp inherited his brother's titles, becoming the 6th Earl Spencer.
Most titles seem to be handed out in pairs - so a Viscount is also created an Baron, or an Earl is also created a Viscount, but they also tend to be piled onto titles already existing. If a peer only has 2 titles then it means that the first holder of their title didn't have any additional titles before hand.
Actually, on that note, the Earl of Snowdon holds 3 titles as well - he was created 1st Earl of Snowdon and 1st Viscount Linley in the Peerage of the United Kingdom for his wedding in 1961, and then in 1999 he was offered a life peerage when the House of Lords was being reformed (he was expected to refuse it, like the members of the Royal Family, but shocked everyone by not), and so is now also Baron Armstrong-Jones.