The phrase "already begun introducing" is correct and usable in written English.
It can be used when indicating that the process of introducing something has started prior to the current moment.
Example: "We have already begun introducing new policies to improve workplace efficiency."
Alternatives: "started to introduce" or "initiated the introduction of".
Already, the House Judiciary Committee has begun introducing a series of bills pegged to certain parts of an immigration overhaul, in a move designed, in part, to press the bipartisan group to action.
They had already been making deliveries through Amazon Fresh and had begun introducing brick-and-mortar stores.
Other member health care systems have already begun to introduce the program at their sites.
Republicans had already begun to introduce measures that would temporarily fund and reopen the museums, monuments, and national parks, so photogenic in their forlorn inaccessibility.
The House committee in charge of the reforms has already begun to introduce piecemeal components of NCLB reform, while senators have said they intend to address NCLB through a single, sweeping bill.
Egypt's Supreme Council of Antiquities has already begun protective measures by introducing ventilation systems and restricting the level of visitors, the New Kerala reports.
To make the Fleming amendment seem necessary, a propaganda campaign had already begun before the amendment was introduced.
Samsung may have already begun to do that: Last week, the company introduced a new smartphone, the Galaxy S III, which includes an improved version of its Music Hub cloud service.
Freightliner, part of DaimlerChrysler, will introduce it late this year and has already begun promoting it to American off-road driving enthusiasts who own smaller military surplus Unimogs from Europe.
Determined to introduce motion into painting, Mr. Breer had already begun making stop-action films, titled "Form Phases," based on motifs from his paintings.
