There’s generally no limit on how many savings accounts you can have across multiple providers. However, to keep things manageable, it may be best to limit it to one or a couple of accounts. One strategy could be to have one account with a high bonus interest rate (even if it has conditions attached), but to also have some savings in an account that offers a relatively high base interest rate.
That way if you miss out on the bonus interest, you will still be earning some interest via the base rate.
If you have more than $250,000 in savings, you may choose to spread your savings across multiple providers, as your deposits are only guaranteed by the government up to $250,000 with any one provider.