Hindi and Urdu are very similar languages, written in Devanagari and Arabic, respectively. The Uighur language in western China has 4 different writing systems in modern use, and a major historical literary tradition in a fifth alphabet. The historical Uighur writing system is descended from the Sogdian alphabet, and it was adopted by the Mongols and became the predominant writing system of the Mongol empire, as well as the Manchus. Starting in the 10th century, Uighurs became Muslims, and started writing their language in the Arabic script. At the start of the People's Republic of China, the PRC attempted to discourage Muslim influence, and encouraged the Uighurs to write their language using Cyrillic (Russian) letters. However, in the 1950s the PRC started to have tense relations with Russia, and enforced a rule that Uighur children should be taught to write their language with the Latin alphabet. In 1982, China decided to return the Uighur language to the Arabic alphabet. Now, in order to use ubiquitous latin-alphabet keyboards, many young Uighurs are using a latin characters to write their language, but with different conventions from the pre-1982 version of romanization.
So, to summarize: a young Uighur today will read newspapers in the Arabic script, and text his friends with the latin alphabet. His father will write using the latin alphabet in a very different way. His grandfather will write in Cyrillic, and, if he's a scholar, he'll read old books in the ancient Uighur script.
And then there's Japanese, which will mix three different writing systems within a single sentence in a modern newspaper: logographic kanji alongside syllabic katakana and hiragana.
There are many, many other similar examples around the world.