New Current account without switching

[Imfat]

We would like to open another current account for every day banking leaving the original one for the bills/direct debits.
At the moment the original one has my DH works pension, state pension and my small income.
After April I'll be retiring and my statement will be hopefully paid in the new account for every day spending.
Can we have two current account with the same bank or should we go somewhere else.
We only have nationwide and the post office in town. Next big town is 15 miles away but we want it online

I've got 3 current accounts with Nationwide, 2 current accounts with the Bank of Scotland , and 3 current accounts with the TSB. And also current accounts at various other banks. I hasten to add they were opened at various times over the years to take advantage of various interest offers and I don't use most of them much, apart from keeping them ticking over.
So I've never had a problem opening current accounts. And I've never switched. Most of my standing orders go off my original long term account that my income goes into.

If i were you I would shop around because some current accounts give access to certain savings accounts and other benefits.

I do similar to what you are proposing.
I have a nationwide current account where all money is paid into. I leave what I need to pay bills with in there. I then transfer the rest between my savings and my Chase current account which I use for everyday spending. It means I can keep track of everything. I originally got Chase for the 1% cashback offer (which is only on limited things now) but was easy to set up and have had no problems with them. If you are ok with online banking I'd recommend.

I have four - Halifax which I opened aged 18 as it had the best student offer; this still continues as my main account,, Co-Op Bank joint account which we use to pay our bills and the mortgage, Nationwide which I opened when we had a Nationwide mortgage (and keep open because I value having a local branch I can use) and Chase which I opened because it is (or was) best for spending abroad and has 1% cashback on food spending.

Its worth having them with more than one institution as there have been occasions when particular bank networks have gone down so people couldnt use their cards etc.

Its worth shopping around as different banks have different offers/ features and access to other products such as linked savings accounts etc. Some will insist that switch everything to them to get the best deal but many like Chase dont make you shut the other one