OK. Found something useful on KFF.org (Kaiser Family Foundation). From their Q and A section referring to signup for 2016 plans :
I signed up for a health plan at the beginning of Open Enrollment, then changed my mind. Can I switch to a different plan as long as the Open Enrollment period hasn’t yet ended?
Yes. You can switch to a different plan at any time during Open Enrollment.
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Sounds like Jim was right!
And I am assuming the Open Enrollment period is one period from Nov 1 2015 through 1/31/2016, as opposed to one of the 3 sub-enrollment periods.
Too bad for the first insurance co that created your cards, and set you up in their system, etc. Oh well.
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And from healthinsurance.org :
Q. If I already enrolled in a plan for the new year, can I change my mind and pick a different plan instead?
A. Yes, you can make multiple plan selections during open enrollment, as long as you complete the final plan change by the end of open enrollment. This applies to people whose prior-year plans were
auto-renewed, as well as those who selected their own plan for the new year and want to make a different choice instead.
In almost all states, plan changes completed by the 15th of the month will be effective the first of the following month.
There are three states that have deadlines after the 15th of the month to get a first of the following month effective date:
Massachusetts,
Rhode Island, and
Washington all allow consumers to enroll or make a plan change up until the 23rd of the month and still have a first of the following month effective date.
If you enroll in a plan early in open enrollment and then change your mind before open enrollment is over, contact the exchange and follow its instructions for making a plan change. Make a note of who helped you, and get an incident number to keep track of the steps you’ve taken.
Be aware that the cancellation of your existing policy could take a while, especially during
open enrollment when the exchanges and carries are very busy. Generally, if you enrolled through the exchange, you have to initiate the cancellation request through the exchange, and they’ll transmit it to the carrier. (If you’re enrolled in an
off-exchange plan, you’ll submit your cancellation request directly to your carrier.)
If your current premiums are automatically drafted from your bank account, you can request a change to paper billing; in most cases, this can be done directly through the carrier. Then, if there’s a delay in processing your cancellation request, you won’t be inadvertently paying for two plans at the same time.
Make sure you pay any premiums due on the current plan to cover you until the new plan takes effect, so you don’t end up with gaps in coverage.
After the end of open enrollment, you won’t be able to make a plan change (including off-exchange, unless you live in Nevada) for the rest of the year unless you have a
qualifying event.
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Note that it says you have to call the Obamacare people to make the change. Can't do it using the system, supposedly.