Can we limit a trial period to specific customers on a plan?

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Yes, a great way to handle this would be through the use of the Trial Coupon discount type. Free trial coupons can be used to give new subscriptions different free trial lengths. Free trial coupons can also be redeemed on new subscriptions to plans that don’t normally have a free trial, although merchants will not be able to use the Trial Ending Reminder email to remind customers when their free trial is ending.

A good way to handle this use case specifically is to simply create a trial coupon for your specific plan, then only provide the coupon to the individual customers that you would like to provide the discount to. This ensures that only the select few customers will receive a trial period while the others will signup with the normal plan rules in place.