Unless there is some over-riding requirement (like a Part 135 operation in the US) that mandates the company make up and follow a checklist, it's natural to make up and use your own checklist.
There is no legal requirement to only use the manufacturer's checklist and if you have any optional equipment installed that has a Flight Manual Supplement, and especially one that is not installed at manufacture, then you have to make your own checklist.
Be prepared to defend it!
For the 109E and subsequent models for example, there is no need to go to flight after starting the first engine - the fuel control will maintain the N1 when the governor is turned on, unlike the earlier models.
And it makes sense to only move the two engine mode switches at the same time to prevent the situation of trying to take off with one at idle and one at flight - it's happened many times in the past, and will continue to happen unless you have the discipline of moving both switches at the same time.