If I invest in a stocks and shares ISA with you, can I also invest in other types of ISA?

Yes you can, providing you stick within the annual limit of £20,000. You can choose to use your total allowance in a stocks and shares ISA or you can choose to split the allowance with other types of ISAs. However you must not go over your annual limit in total or pay into more than one ISA of the same type in any one tax year.